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Published hy the 

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l^«^t\«\«\i^C^<^Cf««^tf\«^«\«\tftAtfti\i\A«^i\i^i^«^tf\«^<^i^C^c^C\i^«^A«^i^«^<^c^<^i^i\c\Ai^c^C^c^tf^i^«^ct«\i^tf^«' 



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MECHANICS OF HEATING 
AND VENTILATING 



WITH CHAETS FOR CALCULATION 
AND EXAMPLES 



BY 



KONRAD IJ^EIER 

CONSULTING MECHANICAL ENGINEER 
FOR HEATING AND VENTILATING. 



McGRAW-HILL BOOK COMPANY 

239 WEST 39TH STREET, NEW YORK 

6 BOUVERIE STREET, LONDON, E. C. 

1912 






Copyright, 1912 

BY THE 

McGraw-Hill Book Company 



Entered at Stationers' Hall, London, England 



All Rights Reserved 



'inted and Electrotyped 
by The Maple Press 
York, Pa. 




^CI.A309364 






v^ 



PREFACE 

The theories of heating and ventilating may be brought under 
three general headings: 

1. The movement of fluids. 

2. The transmission of heat or thermal functions. 

3. The requirements of hygiene. 

The first named would treat of the flow of the different heat 
carriers^ and of air for ventilating, with special reference to the 
conditions met in modern practice. It would represent the 
mechanical side, while the heat transmission in its various steps, 
through building structure, as well as in generating or absorbing, 
radiating, and emitting heat, are more purely physical functions. 
In a work on the whole subject of heating and ventilating these 
two chapters could not be strictly separated,- and the third one, 
the sanitary side, should also be considered in relation to the 
others. However, the present treatise is not intended to go 
beyond the first of these three equally important phases. Nor is 
it claimed to be an original contribution. It is presented as a 
collection of data from various sources, sifted, compared and 
selected with the idea of meeting certain needs of the day, and 
put into shape for ready application. At the same time, it has 
been attempted to give a comprehensive and explanatory outline 
of the subject, which may contribute toward friendlier relations 
between theory and practice, for the benefit of those who care, 
and make the data presented more useful to the student and 
engineer, and through them to the public. 

The author is indebted to Mr. Fritz Schiibeler, with Sulzer Bros., 
a pupil and former assistant to Dr. A. Stodola for a friendly 
discussion of some theoretical points, and to his ofiice assistant 
Mr. Alfred J. Offner for the patient and faithful execution of 
the charts. K. M. 

V 



CONTENTS 

THE FLOW OF WATER, STEAM AND AIR IN HEATING AND VENTI- 
LATING PRACTICE 

CHAPTER I 

Introduction 

Page 

The need of systematic calculation 1 

General principles 3 

Previous use of logarithmic charts . 9 

THE FLOW OF WATER 

CHAPTER II 

Theory of the Flow 

Properties of water 11 

Friction in pipes 11 

Local resistances 15 

Velocity head 18 

Total head ' 21 

Motive power 22 

CHAPTER III 

Forced Hot Water Heating 

Chart I 24 

Distribution on a circuit 25 

Effect of throttling 26 

Distribution under reduced head 28 

Heat developed by the flow 29 

Temperature head 30 

Static head in a forced circuit 31 

AppHcation of Chart I 31 

Example 33 

CHAPTER IV 

Hot Water Heating by Gravity 

Charts II, III and IV 37 

Balanced gravity circulation 38 

Effects of throttling 40 

vii 



viii CONTENTS 

Page 

Distribution at reduced capacity 41 

Application of Charts II, III, and IV 42 

General corrections 46 

Individual corrections ^ 48 

The method of piping 50 

Underfeed distribution 50 

Example 51 

Overhead distribution 54 

Example 56 

Single main distribution 58 

Example 60 

THE FLOW OF STEAM 
CHAPTER V 

Theory of the Flow 

Properties of steam 63 

Friction in pipes 65 

Local resistances 68 

Velocity head 69 

Energy expended in flow 69 

CHAPTER VI 

High-pressure Steam Distribution 

Chart V 71 

Outline of the problem 71 

Distribution under varying pressure 73 

Distribution under throttling 74 

Application of Chart V 75 

Example of high-pressure steam distribution 76 

CHAPTER VII 

Low-pressure Steam Distribution 

Charts VI and VII . 78 

Outline of the problem 78 

Application of Charts VI and VII 82 

Wet return system 82 

Example of a wet return system 86 

Dry return system 88 

Example of a dry return system 90 

Example of low-pressure steam heating at 5 lb. pressure 92 

The open return system 94 

Example of an open return system 97 



CONTENTS ix 

THE FLOW OF AIR 

CHAPTER VIII 

Theory of the Flow 

Page 

Properties of air 100 

Friction in conduits 100 

Factors of local resistance 103 

Simple forms of resistance 104 

Equivalent area 106 

Composite resistances 108 

Velocity head 112 

Junctions 113 

Total pressure 120 

Motive power 124 

CHAPTER IX 

Air Blast at High Velocities 

Chart VIII , 125 

Outline of the problem 126 

AppHcation of Chart VIII 127 

Examples of air blast arrangement 128 

CHAPTER X 

Forced Ventilation 

Chart IX 133 

Outline of the problem 133 

Application of Chart IX 134 

Example of forced ventilation 139 

Example of coupHng fans 140 

CHAPTER XI 

Hot Air Heating and Ventilating by Gravity 

Chart X 142 

Aero-motive force for gravity circulation 142 

Outline of the problem 146 

Mean levels 147 

Neutral zones 148 

Correct height of draught 150 

Temperature as a factor 152 

Distribution 154 

Application of Chart X 155 

Example of a gravity vent 156 

Example of indirect heating system 158 



MECHANICS OF HEATING 
AND VENTILATING 



CHAPTER I 
INTRODUCTION 

The Need of Systematic Calculation. — It may seem to be self- 
evident that an intimate knowledge of the natural laws governing 
the movement of water, steam and air in conduits is indispen- 
sable to the heating and ventilating engineer. Nevertheless, it 
will be admitted, that the solution of the ever recurring problems 
of distribution and discharge is still attempted quite generally 
without a true and consistent application of these laws. The 
main obstacle to calculation on a physical basis lies probably 
in the lack of ready made data relating specifically to this field. 
Most of the information is obtainable, but more or less scattered, 
and not in convenient shape for practical use. 

A superficial experience in the field may not convince that the 
scientific method will pay in engineering work of this character, 
but those among the profession who are in the habit of studying 
cause and effect will generally concede that a good share of the 
petty annoyances, of discomfort, and even of suffering brought 
about by indifferently designed heating apparatus can be traced 
to faults in the distribution of the heat carrier. In a ventilating 
system it is also the uncertain delivery, or what may be called the 
lack of control over air currents, that is responsible for much 
vexation, inefficiency and disappointment. Whatever may be 
the share of troubles that can be laid down to other causes, the 
ability to foretell the carrying capacity of a pipe line and to 
assure in advance a fair distribution of the fluid through a system 
of conduits of any complexity and length, would seem to be at 
least one of the prime elements that make for successful perform- 
ance. But aside from the question of obtaining the results, a 
straightforward solution of the problem on a sound basis will 
obviate the need of excessive allowances to cover the lack of 
knowledge, and lead to economy in first cost. It will also con- 

1 



2 MECHANICS OF HEATING AND VENTILATING 

tribute to the efficiency of a plant in operation by avoiding waste 
through overheating and in other directions. 

Thumb rules in general give only an average, which may not 
apply to the case in hand. They should not be relied upon for 
design and construction, but may serve for rough preliminary 
estimates. Neither will tabulated figures cover the requirements, 
if based on a fixed set of conditions, such as the pressure loss for 
a certain length, which hardly ever coincides with a particular 
instance. Such tables ought to be used only for approximate 
sizing. 

For methodical calculation of a conduit it is essential to be 
aware that the fluid to be moved, or kept under control, must fol- 
low the laws of nature. All calculations relating to the flow 
should therefore be based, first of all, on formula giving adequate 
expression to the forces coming into play. This means that each 
case should be studied, not only with a view to applying the 
proper formula, but also in order to size up the various factors on 
which to base the computation. Theory and practice will be 
found to agree if this is done. Whenever they seemingly do not, 
some element has been left out of consideration or a factor has 
been misjudged. 

It is most desirable also to have a clear grasp of the problem as 
a whole in the more complex cases of distribution. For instance, 
it is well to remember that the total pressure differences which 
we depend upon to create the movement are usually equal for 
all points of delivery, while the runs of conduit to these points 
are apt to be widely divergent in length and obstructing features. 
Diameters proportionate to quantity or to pressure drop for a 
uniform length would therefore present very unequal resistances 
for the intended flow. Since the total resistance inevitably con- 
forms to the pressure available, the quantity delivered must de- 
pend on the relation of the resistance head to length of run. 
Technically speaking, the lines of least resistance, which the fluid 
is bound to take, must be made lines of equal resistance by giving 
them a different ^'hydraulic slope," or ratio of head to length, 
for each section of main, or branch, according to distances and 
other features. Translated into popular terms, long conduits 
must be eased by a low rate of resistance and short ones throt- 
tled by a high rate, in order to make up the same total. 

To equalize the head for given volumes involves repeated 
calculation of each portion of conduit by formula on hand of 



INTRODUCTION 3 

certain factors, to be assumed tentatively. The formula3 are 
mostly inconvenient, and their application takes more time and 
patience, even with the aid of complete tables, than is generally 
available. To make the process more popular, it must be sim- 
plified without material sacrifice in accuracy. The diagrams 
presented have been worked out with this end in view. They 
have been tried for several years in actual practice and the results 
have uniformly justified the labor of scientific calculation. Ac- 
cording to the exigencies of the case, the procedure can be ab- 
breviated, or carried further. Every engineer may evolve his 
own methods in using the charts, to suit his needs, but for suc- 
cessful and profitable use of the information presented it is neces- 
sary to be famihar with certain principles of hydraulics. 

General Principles. — The movement of a fluid through a line of 
conduits always represents a certain amount of work performed, 
or of energy converted, which can be expressed in terms of heat or 
of mechanical power. If the drop in tension is knowm, the work 
can be computed in foot-pounds, as the product of volume of the 
fluid per time unit and pressure against which it moves, that is, 
by the product of distance and weight. Usually the volume is 
the given quantity from which the pressure is to be calculated. 
The latter is made up by the various resistances presented by 
conduits, and by the momentum of the flow, or the motion itself. 
The idea is best recalled by Fig. 1, familiar through all text- 
books on hydraulics. It may serve here for reference and expla- 
nation of the terms and symbols used in this treatise. 

According to the law of gravitation it is always the height H 
through which a fluid drops, or a pressure P equivalent to the 
weight of that column for a density w, that determines V, the 
theoretical velocity of fall or of frictionless discharge through a 
rounded orifice. The actual velocity in a conduit is always 
smaller, owing to the friction and the resistances offered by 
throats, elbows and other features, which take a certain definite 
head to overcome them, and may be expressed in terms of pres- 
sure or height Pf and pj., or hf and h^.. The difference between H, 
the total head available, and Hf + H^, the combined resistances pre- 
sented by the conduit, gives H^, the net effective head exerted by 
the moving fluid, or the velocity head, as measured by the Pitot 
tube. From this can be figured the actual velocity of discharge 
V = \/2gH^, which gives the volume of the fluid Q for the conduit 
area a. 



4 MECHANICS OF HEATING AND VENTILATING 

The resistance by friction and obstruction or local resistances, 
both representing lost motion, retard the flow to a greatly varying 
extent, according to the length and character of the conduits. 
Either of these items may be the major portion of the total head 
and control the situation. In other words, the final speed of 
delivery for the same head H and volume Q may range from the 







1 
»__i 

H 

1 
1 




1 

^f 


~~[S 









K 




— 


-4 ^^ 

1 =r 


V 


ir_z~_^ 


1 1 

1 \/ i 


A'^ 





'■ 


T 


K^ 




-4^ 



Fig. 1. — Diagram of the flow of liquids in conduits and explanation of terms and symbols. 

H = Total or theoretical head, in ft. 
Hf = Total head to overcome friction, in ft., or 2 hf. 
Hr = Total head to overcome resistance, in ft., or ^'h,-. 
Hv = Total head to create actual velocity v, in ft per sec. 

w = Density of fluid, or weight per cu. ft. 

P = Hw= Pressure in lb. per sq. ft. 

V = Theoretical velocity in ft. per sec. =A^2gH = -^ 2g- 



v = Actual velocity in ft. per sec. 



Q 



= V2gH = iJ 



Q = Volume of fluid per sec. 



V V 

W = Weight of fluid per hour = 3600 w Q. 
d = Diameter of conduit. 1 = Length of conduit in ft. 

c = Circumference of conduit. f _ Coefficient of friction. 

Q 



Area of conduit in sq. ft. = — 
^ V 

Q 
V 



A = Equivalent area in sq. ft. 



r= Factor of resistance. 
g = Acceleration (32.16). 



full theoretical velocity V down to nothing, while the conduit 
increases from the frictionless orifice for V, or the equivalent area 
A upward, indefinitely, depending on the resistances opposed to 
the flow. 

The basic formula for friction applies equally to any fluid. 
The loss of head for a run of conduit of uniform cross-section, 
according to the generally accepted theory, is expressed by 

hj = f — — 



INTRODUCTION 5 

for any shape or cross-section of conduit, or 

' 2g d 

for round pipes only. 

The velocit}^ corresponding to the area and volume transmitted, 

v = — , is assumed to be the mean velocity within the conduit, the 
a 

flow being more rapid in the center than at the circumference or 

surface of contact and always more or less turbulent above a 

certain speed. The friction naturally depends on this turbulency, 

or the internal losses of motion, which are known to vary with 

different ratios for , the hydraulic radius. It is also influenced 
c 

materially by the character of the contact surface, the viscosity, 
and the velocity itself. All these factors have been shown to 
bear on the coefficient of friction f, under conditions met in 
ordinary practice, but to a varying extent for water, steam and 
air. The above formula is therefore only applicable in connec- 
tion with additional data giving the proper value of f for the 
fluids in question and for the kinds of conduit used. The values 
given for this coefficient by investigators for various conditions 
is more or less conflicting, and much of the data does not apply 
to speeds and conduits met in heating and ventilating practice, 
hence the engineer is often left in doubt as to the proper value 
to be used in a given case. Other formulae which express these 
variations directly by composite constants are inconvenient. 
This difficulty is avoided by Tutton's general form 

v = CR^Sy 
which includes the bearing on f of the hydraulic radius R, and 

the slope - or S, through the odd exponents x and y, and there- 
fore can be made to apply at least for one kind of contact surface 
and the same viscosity, that is, it will be correct for a range of 
areas and velocities covering an entire field, either water, steam 

or air. If we substitute — or -- for R, -— for S and call the con- 
1 c 4^ 1 

stant — Y — ^7 "^^6 formula reads 

ir(T)'--f 



6 MECHANICS, OF HEATING AND VENTILATING 

This formula is, of course, not convenient for working purposes, 
but the values derived from it can be charted in straight lines on 
logarithmic paper. The exponents of hydraulic radius and slope 
are thereby expressed by the slant of the lines of diameter and 
velocity, which differs, as stated, with the viscosity and rough- 
ness of surface. A glance at any of the charts will show at once 
the interrelation of pressure, volume, velocity, and area. Two of 
the factors known will determine a point of intersection and give 
the value of the other two. Thus, for instance on Chart IX, a 
volume of 25 cu. ft. of air per second moving at 12 ft. velocity 
will require an area of 300 sq. in. and cause a pressure loss of .27 
lb. per sq. ft. per 100 ft. of length. 

Separate charts are necessary to cover the flow of water, steam 
and air, but this would be desirable in any event, in order to give 
the quantities in the customary measures. The three principal 
fields have been further divided with the idea of presenting dis- 
tinctive classes of work to best advantage, each chart being 
worked out only for the needed range at the largest scale practi- 
cable for publication. It has been possible in this way to bring 
much data together, to assign to it its proper sphere, and to 
make it ready for use. The sources of information on which the 
charts are based are stated in the chapters on water, steam, 
and air. 

Reliable and pertinent information on local resistances due to 
various forms of obstruction is much less complete than that 
for friction, although it is often quite as important for calculation, 
and should receive equal consideration. Usually, an item of local 
resistance is expressed as a function of the velocity head 



V 



' 2g 

wherein r is the coefficient of resistance intended to measure the 
degree of obstruction presented to the flow by various features, 
such as bends, irrespective of size. According to experimental 
evidence, this expression is not strictly correct, and should be 
considered only as a general approximation. Present data on 
the point is too scant to permit definite conclusions, but there 
are sufficient figures available to indicate that the loss of head 
also depends on the diameter of conduit and the velocity. Con- 
sidered as a degree of friction, which is also loss of motion 
through uneven conduit surface, it seems logical that such resist- 



INTRODUCTION 7 

ances would follow the same general law and might be expressed 
in a way similar to Tutton's formula. This theory is strengthened 
by the fact that the coefficients of contraction are known to 
vary with diameter and velocity. All forms of obstruction 
involve more or less contraction of the stream, hence it is 
reasonable to assume that the loss of head may be stated by a 
formula similar to Tutton's 



K=c.T-^ 



d 



with the exponents for v and d to be determined for different 
classes of work. This mode of expression would require separate 
charts giving the resistance head for any diameter and velocity. 
Inasmuch as the bearing of v and d on the factor appears to be 
less pronounced than it is for friction, a fair approximation can be 
obtained if the formula is simpHfied to read 

1 

hr = C.r-- 
2g 

and by taking the exponents for v equal to that for friction. 
This form permits the losses of head by local resistances to be 
plotted on the same chart, by lines of different colors or character, 
parallel to those for diameters, and giving the values for individual 
items, not for any area, but for any velocity. The readings are 
thus made decidedly more convenient, as the pressures for friction 
and several features of obstruction for a run of even area may be 
read from the same velocity line, without straining of the facts 
beyond the probable limit of error. These items of resistance, 
at best, must remain an uncertain quantity owing to the individu- 
alities of commercial forms and features. As presented, the 
results should be, on the average, at least as accurate as general 
data applied to special cases. 

In order that r should express the relation of the resistance 
to the corresponding velocity head, the constant C has been 

v2 
made to equal — for a velocity at which the generally accepted 



V 



coefficients of resistance would fairly apply. For v = l, C would 

V v2 

be — = 1 and the head h^. = r — , but the values for all higher 



8 MECHANICS OF HEATING AND VENTILATING 

velocities would be less than the function of — . It is probable 

that the average of experimental data on r has been derived at 

higher velocities and is more nearly correct at 10 ft. p. s. On 

this assumption the constant C has been made to equal about 

102 .. . 

in the applications of the formula to water, steam and air, 

lo^y 

thus giving higher average values throughout, which are ex- 
pressed in the formula for h^ by different constants. 

The velocity head is charted on each diagram by a line of 
definite slope, giving at a glance the accurate value of 

v2 v2 

H„ = — or of P,, — w — , for any speed. Vice versa, houi a known 
. . 2g _ " 2g' -^ ^ 

rise in a Pitot tube we can read directly the velocity at which the 
fluid must be moving. The line is also most convenient for the 
frequent readings of the dynamic head, or momentum of the flow 
incidental to duct calculation, especially in connection with its 
bearing on the flow at junctions or through contractions and 
enlargements of conduit, and wherever the correlation of static 
and dynamic head may enter into the problem. It can also be 
used conveniently to determine the so-called equivalent area A 
corresponding to the pressure at any point of the conduit. The 
intersection of this line with that of H or P gives the theoretical 
velocity V, and the area corresponding to that speed and the 

. Q . . Q 

volume is — = A, which must be distinguished from — = a. The 

V V 

former. A, represents the smallest, or theoretical area through 
which the volumes could pass, while the latter, a, designates the 
actual area, which must be greater, according to the resistance 
to be overcome. This equivalent area or orifice is commonly 
assumed to be an opening in a thin plate, with sharp edges, giving 
a contracted stream and allowing for this contraction according 
to the coefficient of effiux. Blaess,^ who applies the term to his 
method of duct calculation, suggests the rounded frictionless 
outlet as a more definite basis. In the present treatise A refers 
also to the theoretical frictionless orifice. 

The total head is represented on the charts in different ways, ac- 
cording to the field of application. With forced calculation of 

^ Dr. Ing. Victor Blass, "Die Stromung in Rohren," Oldenbourg. 



INTRODUCTION 9 

air and water it gives the power i-eqiiirements, and, incidentally, 
the theoretical head that a machine must produce, together with 
the corresponding velocity and blast or equivalent area. That is, 
it provides the correct basis for the calculation of centrifugal or 
other machinery for propelling the fluid. On the table for grav- 
ity hot air heating and vents, the available total head, varying 
in each case, is charted for a liberal range of conditions. For 
steam and hot water heating where the total head is usually pre- 
determined, an auxiliary table is worked out for convenient 
approximation, or for tentative sizing, as a basis for final accu- 
rate calculation. 

The charts, in addition, give the special data for balancing 
gravity hot water heating systems, and the principal factors for 
correction applying to unusual and variable conditions, as far 
as it will pay to consider them. They give also the means for 
rapid, but consistent, approximation, and for the quick reading 
of the simple relations of area, speed and quantity. 

The true usefulness of the charts depends, of course, upon a 
clear grasp of the problem in hand, as for instance the delivery 
of fixed volumes at certain points with a uniform pressure drop, 
which would be a problem in equalization, or of delivery against 
different heads, a case of balancing. The charts will be found 
to provide the necessary facilities to apply the mechanics in 
every-day practice. 

Previous Use of Logarithmic Charts. — Similar charts have been 
w^orked out for various special purposes more or less related to 
heating and ventilating, and covering small parts of the field. 
Among these may be mentioned the diagrams on the flow of 
water in channels by Prof. I. P. Church^ and the diagrams by 
Schoder^ and Bleich^ for the flow of water in pipes. Birlo, a 
German heating engineer years ago applied the principle to hot 
water heating. These tables are now reissued in a new form, 
though not on a logarithmic scale, by Schweer.^ Gremmels has 

^ " Diagrams of Mean Velocity of Uniform Motion of Water in Open Chan- 
nels." Irving P. Church, C. E. John Wiley & Son. 

2 " A Diagram for the Flow of Water in Pipes. " E. W. Schoder, Engineer- 
ing Record, Sept. 3, 1904. 

^ " Hydraulic Diagrams for Circular Pipes." Samuel D. Bleich, Engineer- 
ing Record, Vol. LVI, No. 22. 

* Schweer, '' Graphische Rohrbestimmungs Methode fiir Warmwasser- 
heizungeen." 



10 MECHANICS OF HEATING AND VENTILATING 

applied the principle to low pressure steam heat.^ Gramberg 
has compiled a series of tables for hot air and water heating which 
include also data for giving the total head available in gravity 
work. 2 A collection of similar tables for water pipes and channels 
has been issued by A. Gremand.^ 

The charting on logarithmic paper for such purposes is capable 
of being improved and extended to other lines of work. In fact, 
the possibilities of this method of calculation are only beginning 
to be appreciated. The idea underlying the slide rule is here 
applied to specific purposes, permitting the direct reading of 
values, otherwise calculated by formula, for a given range of 
factors which can be extended indefinitely by mere elongation of 
the lines. No auxiliaries, such as scales, planimeters, dividers or 
other tables, are necessary. On the whole, the graphic method 
should contribute materially to efficiency in engineering by en- 
couraging the true and yet practicable solution of a problem. 

The intention has been to make these diagrams cover as closely 
as possible the special requirements of engineers for heating, 
ventilating and similar work and with particular reference to 
modern building practice. By way of explaining the applica- 
tion of the charts to best advantage, a general treatment of the 
mechanics relative to this special field is presented in the follow- 
ing pages. 

^ "Tafel zur Berechnung der Druckverluste in den Dampfieitungen ftir 
Niederdruck Dampfheizungen" Gesundheits Ingenieur, 1905. 

2 See "Gesundheits Ingenieur," No. 27, 1907. 

^ "Graphische Tafeln zur Bestimmung der Dimensionen von Wasser- 
eitungen und Kanalen." 



THE FLOW OF WATER 

CHAPTER II 
THEORY OF THE FLOW 

Properties of Water. — The weight and volume of water at dif- 
ferent temperatures, the specific heat and the boiling-points under 
v^arious pressures, are presented by a diagram in place of the 
customary table of properties, which will permit readings down 
to any fraction desired in practical work and without the neces- 
sity of interpolation. 

The density curve is based on Nystrom's computations from 
experiments by Kopp, as given in Supplee's '^ Mechanical Engi- 
neering." The boiling points are given for various pressures, 
expressed in water columns at respective temperatures and in air 
columns or elevation above sea level. The equivalent pressures 
in pounds per square inch and vacuum in inches can be found on 
the steam table. Separate scales are given for pressure per 1 ft. 
of height, and reciprocals, from which the accurate pressure for any 
height, at any temperature can be figured. The lines for total heat 
above 32° F. are made to correspond with the recent investigations 
by Diederici,^ which follow Regnault's figures closely at least up 
to about 300° F. The unit of heat is taken to be the mean value 
between the freezing- and boiling-points. The B. t. u. therefore 
give the accurate amount of heat for any rise in temperature by 
subtraction. 

Friction in Pipes. — Of the numerous formulae for the flow of 
water in iron pipes, Schoder's application of Tutton's general 
expression, quoted in the introductory chapter, consistently 
renders the bearing on the friction head of the pipe diameter and 
the mean velocity of the flow. For wrought iron pipe he finds^ 

v = 174R-5^ ar hf = .00038 1 '^ 



The exponents for v and d are the result of an extended series of 

^ " Die Calorischen Eigenschaften des Wassers und seines Dampfes." Zeit- 
schrift des Vereins Deutscher Ingenieure, 1905, p. 362. 

^ See Engineering Record, Sept. 3, 1904 and "Trans. A. S. C. E.," 
Vol. LI, p. 308. 

11 



12 



THE FLOW OF WATER 



Z.50 



Head in Ft. of Water per llb.persq.in Pressure 
245 i-40 2.35 

n — 1 — \ — r 



soot 



1 — 1 — I — I — I — r 

Volume of Water per lb. in cu. Ft 
0173 .0172 .0171 .0170 .0169 .0168 .0167 0166 .0165 0164 



1 — I r 

.0163 .0162 



.0161 OieOcaFt 




400 



53 60 61 

Density, or Weiqtit percu. Ft in lb 

I I I I I I I I I I I 



AlO .420 

Pressure in lb. per aq. I'n for I ft Head of Wa ter 

Diagram A. —Properties of water 



familiar formula hf = f „ ,-. Schoder's value for C is therefore a 



THEORY OF THE FLOW 13 

experiments, and may be accepted as covering the variations of 
the coefficient of friction given by various authorities for the 

v2 1 

2gd- 

constant for one kind of pipe, and his exponents for R and S are 
correct for the same viscosity. When modified to read 

yl.86 \ 

hf = .0245 

f 2g d^-25 

Schoder's form will show its relation to that used by Weisbach. 
It will be apparent that for v = l ft. and d =1 ft., the constant 
.0245 should be equal to the old variable coefficient. Weisbach 
puts f at .0316 for 1 ft. velocity at any diameter, but his experi- 
ments were made on small sizes (3/8 in. to 1 in. only),^ for which 
the newer formula will give even somewhat higher values. 

To provide a safe margin for commercial pipe, as used in heat- 
ing work, and assumed to be in fair condition, also to allow for 
the extra resistance of ordinary couplings, the constant .00038 

has been rounded up to .0004 or to '- . The friction losses 

2g 

on the charts are plotted on this basis with the velocities figured 

for the actual inside diameter of standard weight wrought iron or 

steel pipes. 

For ordinary ranges the friction heads will be found to check 

fairly well with those derived from Lang's, Weston's, D'Arcy's, 

Fanning's, Tutton's, Hazen- Williams' and Pelton's rules and 

tables, but due allowance must be made in comparing, for the 

varying range and conditions for which the figures are intended 

to apply. The charts also agree closely with German data for 

heating practice, except for small pipe sizes, for which Rietschel 

in his treatise gives a somewhat lower friction head. Later 

experimental data from the same authority show the discrepancy 

to be smaller, and the most recent information gives lower values 

throughout, but presumably for new pipe, tested under ideal 

conditions. The formula by Ganguillet and Kutter, which is 

widely recognized, on the other hand, gives still higher friction 

head for the same diameters, probably allowing for a greater 

amount of fouling than is met with in heating practice. Unwinds 

coefficients, as published in his recent treatise on hydraulics, 

1 See " Weisbach's Mechanics, " p. 867. 



14 THE FLOW OF WATER 

give smaller friction head throughout, based, however, on new 
wrought iron pipe. 

Considering the number of factors that come into play, a closer 
approximation of the data available is hardly to be expected. 
Even within the limits of heating practice the roughness of con- 
tact surface will change, and modify the constant. It is probable, 
also, that the velocity, especially in gravity hot water circulation, 
is often within or below the critical stage at which the motion of 
the water is supposed to be parallel, and the friction head pro- 
portional with the speed. The range of velocities at which this 
might occur depends, however, on pipe diameter as well as the 
frequency of fittings and joints. The latter will practically 
always keep the water in turbulent motion, on which formulae 
on friction head are based. Hence it is not advisable to base 
calculations upon such favorable but uncertain phenomena. 

The changes of viscosity with the temperature of the water, 
according to recent investigations by BieP would seem to have 
an appreciable effect on the friction head, also depending on 
diameter and velocity. For heating work this would have greater 
bearing than is the case in other fields. Unfortunately, experi- 
mental data on this point is very incomplete. Saph and Schoder 
have demonstrated the fact for the range between 40° and 72° F. 
Rateau,^ on the other hand, has experimented at high tempera- 
tures, and pressures near the point of evaporation, at which he 
finds the sudden variations of density, due to pressure changes 
to make the losses of head "extremely interesting." They would 
be difficult to determine for practical purposes even if more data 
were available. Except for artificial circulation, this range is 
outside of conditions met in hot water heating, but the experi- 
ments in general point to the fact that the friction head decreases 
about evenly between the freezing- and boiling-points. 

Whatever the weight of these considerations may be, it will not 
pay to express them by additional lines or corrections. The 
charts will be more serviceable in the simplest form, intended 
to represent average conditions and to be within the probable 
limit of errors from other factors. In problems of equalizing or 
distribution such differences would affect all parts alike, and 

^ "Mittheilungen iiber Forschungsarbeiten," Heft 44, Verein deutcher 
Ingenieure. 

2 A. Rateau. "Recherches experimentales sur recoulement de la vapeur 
d'eau, suivies d'une note sur I'ecoulement d'eau chaude." 



THEORY OF THE FLOW 15 

would have no bearing on the result. In problems of discharge, a 
small error in the friction, as one item in the total head, will not 
mean the same, but a still smaller discrepancy in the volume 
carried. 

Local Resistances. — The assumption explained in the general 
introduction, that the coefficient of resistance decreases with the 
velocity, as the coefficient of friction, when applied to water, 

yl.86 

make the formula for the loss of head h„=1.38 r . The 

2g 

V2 

constant 1.38 represents the ratio of : for v = 10 ft., so that 

yl-8b 

V2 

h_ would be a function of — at that velocity, and would assume 

2g 

somewhat higher values for lower speeds, and vice versa. Taking 
for instance on Chart I the resistance for an open bend, for which 
r = .42, we find the loss of head at 10 ft. to be .65 ft. which equals 

y2 ^ Y2 y2 

r — . At 5 ft. the chart gives — = .38 ft., and r — would be .42 X 
2g ^ 2g ^ 2g 

.38 = .16 ft., while the direct reading of hj. for that form on the 
line of 5 ft. velocity is .175 ft. As stated previously, this increase 
in values is justified, partly on experimental grounds, and also 
because the factor r should be somewhat greater for small size 
fittings in which the velocities are generally lower. The charts 
are thereby simplified while presenting values at least as accurate, 
on the average, as usually obtained by formula with coefficients 
to be selected in each case. The practice of expressing resistances 
of elbows or other features in equivalents of pipe lengths, is good 
for only one size, and when expressed in diameters it is strictly 
correct only at one velocity. These rules; therefore, are likely 
to be less accurate than the values obtained from the charts. 

Little data is available giving the coefficients for the standard 
designs, or even the average types of commercial fittings and 
valves. Weisbach's formula^ for bends and deflections of differ- 
ent radius, at different angles and his coefficients of contraction, 
apply to the ideal shapes rather than to commercial forms. His 
own findings indicate that the common style of fittings, as shown 
on Fig. 2, with shoulders exposing the butt end of pipes, and 
a considerable and sudden enlargement of area. 



See Weisbach's " Theoretical Mechanics " p. 896. 



16 



THE FLOW OF WATER 



involves materially greater resistance than the ideal shape would 
offer. 

The factors of resistance for the various forms of obstruction, 
as given on the diagram, has been obtained by adding to Weisbach' s 
theoretical figures the probable effect of sucli retarding features. 
For recessed and for flanged fittings, flush with the piping on the 




Fig. 2. — Typical cast iron fittings. 

inside, this does not apply. In such cases about 25 per cent, 
may be deducted from the head as charted. 

The values for the factor r thus obtained check fairly well with 
such meager data as can be found for typical shapes and designs, 
but are higher throughout than those adopted by German authori- 
ties which seem to be based onWeisbach's experiments. Accord- 




FiG. 3. — Recessed sweep fittings. 

ing to the latest information on experiments m progress these 
German factors appear indeed to be taken too low. 

Inasmuch as they can only be approximate, the various factors 
have been rounded up, reduced in number and grouped together 
in order to avoid multiplicity at the expense of clearness. Thus, 
it happens that a T fitting without reduction on the run is repre- 
sented to give the same resistance, straight ahead, as the long 



THEORY OF THE FLOW 17 

sweep elbow. An ordinary T fitting reduced by one size on the 
run, will be about equivalent in obstruction to an open bend, and 
a T reduced two sizes, to a close elbow. For greater reduction r 
may be assumed to equal about the head lost by the partial ex- 
pansion and subsequent sudden contraction of the area within the 
fitting which approaches the velocity head in the smaller end. 
If the reducer is a taper piece, the contraction is partially avoided, 
and the same factor as for a straight tee will apply. Likewise, 
for a reducing elbow the resistance is practically that for 
an ordinary elbow, based for safety on the velocity at the small 
end. A junction at right angles includes the velocity head 
which must be created again out of the static head, in ordinary 
fittings without gradual change of direction. This item is to be 
added to those for the branch, as indicated by the line of resist- 
ance on the diagram, which is always drawn through the part 
in question. The factor for radiators is a composite, including 
the velocity head to be entered, in addition to the estimated 
obstruction of two angle valves and the sections, all of which 
generally occur together in the calculation. If one valve and 
one elbow are used, the resistance can be figured by subtrac- 
tion, but this will hardly pay since the difference is a small frac- 
tion of the item as a whole. With uneven sizes of flow and re- 
turn pipes, it is convenient and accurate enough to take one-half 
of the reading for the velocity of inlet, and one-half for that of 
the outlet, giving together the mean value of the two. The 
velocity head is also included in the factor for boilers, which are 
assumed to present somewhat more obstruction than a simple 
tank, allowing for the friction in nipples or headers. Since the 
loss of head is based upon the outlet velocity it is advisable to 
round up the figure for small boilers with large outlets, giving a 
proportionately high velocity through the sections. Coil heaters 
with headers, having the water passage arranged in series of 
liberal area, will present about the same resistance as a radiator. 
When made up as a continuous single pipe coil, the latter it to be 
figured as part of the pipe system. Heaters with coils for steam 
may be assumed to present the same resistance as a tank. In 
every case the factor r must be understood to refer to the velocity 
at the outlet, as indicated by the dash lines, drawn through the 
respective parts. 

The factors for other forms of obstruction can readily be esti- 
mated by comparison with those at hand. Elbows with 45 



18 THE FLOW OF WATER 

degrees deviation give somewhat more than half the resistance of 
a 90 degree turn of same radius, and larger angles less, when in the 
same plane of deflection. For ordinary practice it is permissible, 
however, to assume the factor for an ordinary, close 45 degree 
elbow to be equal to that for a 90 degree medium radius elbow. 

Velocity Head. — As an item in the sum of losses making up the 
total head, the velocity head is generally understood to be the 
balance expended in discharging the fluid. In heating practice 
the water is nearly always returned, or moving within a closed 
circuit, for which this balance remains unexpended while the 
movement takes place. The velocity head in the ordinary sense, 
as the resultant force of movement, does not enter, therefore, into 
the calculation of the total, except where the flow along the cir- 
cuit is interrupted by enlargements of area, as represented, for 
instance, by a boiler or radiators in which the movement prac- 
tically stops. The losses of head incidental to such features must 
be considered. As mentioned above they are included in the fac- 
tors charted. 

For unusual conditions, such as interruption of the movement 
for parts or the whole of the circuit, the momentum of flow to be 
created will temporarily bear on the result, but in ordinary prac- 
tice it is not necessary to consider this. 

The dynamic head and its relation to the static head should 
nevertheless be borne in mind. It should be calculated some- 
times for the purpose of estimating the factors of resistance for 
odd forms of obstruction, and considered also in its bearing on 
the flow at junctions with very unequal velocities. 

In the case of sudden enlargement of pipe area the factor is 
expressed by the Carnot-Borda formula,. which makes the loss 

(v-Vi)2 
hj.= . If the enlargement is gradual, the loss may be 

reduced to a negligible item. The same applies to contraction of 
pipe area, for which the resistance can be avoided by rounding 
the throat, the idea being to convert static into dynamic head, 
and vice versa. These factors, like the resistance in a nozzle or 
a ^'Venturi'' tube, may differ considerably with the direction of 
the flow for the same shape. Wherever possible, the shapes 
should conform to the natural flow. In other words, they 
should be designed to avoid eddies or loss of motion, and 
thereby practically eliminate resistance. 

The velocity head maintaining at junctions will modify occa- 



THEORY OF THE FLOW 



19 



sionally the losses for branch T's at right angles, as taken into 
account by the charted item of resistance. The latter gives an 
average value of r = 1.33, allowing for contraction as well as loss 
of motion. This factor will apply when the flow in the branch 
is not materially slower or faster than that in the main, that is, 
when the component of velocities does not deviate radically from 
the direction of the branch piece. With higher velocity in the 
branch, for which the natural direction of outflow nears the right 
angle, the factor may be taken smaller, since the motion lost in 
the main is relatively smaller, and that in entering the branch is 
fully taken into account. If, however, the flow in the branch 
must be at decidedly lower velocity, a right angle fitting will 
produce a relatively greater resistance, as the natural outflow is 
tending in a forward direction which the ordinary T fitting will 
not meet. It is proper in such cases to allow for greater loss of 
head, or to use sweep or Y fittings to ease resistance. The factor 




Fig. 4. — Two types of branch T's. 

is thereby reduced and may be assumed as equal to that for a 
turn of corresponding radius. This rule will not apply, of course, 
when the side outlets of such fittings are of the full size of the 
main, and bushed down or reduced suddenly by a blank head 
threaded for a smaller size. For such fittings, in fact, a greater 
allowance should be made than for ordinary T's, since the latter 
have slightly eased throats, while the blank head creates eddies 
in a dead space with full contraction at the outlet. This form of 
branch piece, improperly called a '^fitting," is a very uncertain 
factor of resistance, since the attempt at deflection by a sweep, 
with subsequent contraction, is worse than useless. The oppor- 
tunity for air to collect is a further drawback of such shapes. 

Stated in a general way, the relation of static and dynamic 
head at junctions should be considered, and at least roughly 
expressed by the style of fitting. Wherever the factors for 



20 



THE FLOW OF WATER 



average conditions would not fairly apply, a pattern should be 
selected that will suit the case. With high velocities near the 
end of a line, and little static pressure left it is advantageous, 
for instance, to utilize the vis-viva or force of the main flow as 
much as possible for the branches by styles of fittings easing the 
resistances. This is recommended to reduce the uncertainties 
of distribution, quite aside from the waste of energy that may be 
involved in certain cases. On the other hand, when the static 
head is comparatively great, it is a mistake to try to induce dis- 
tribution by deflecting the currents rather than by using proper 
area of pipe. The former mode is often wrongly attempted in 
gravity hot water heating. On mains where the velocities are 




2-- 




b c 

Fig. 5. — Methods of running branches from risers. 




greatest and the losses should be kept down, it will pay to ease 
the flow by sweep bends, by the use of gate valves and other 
means. On rising lines on the other hand, where the head avail- 
able for the upper stories is usually ample, it is proper to use such 
pipe sizes that will make up the desired, easily figured resistance, 
rather than obstructing the flow by extra turns as indicated by 
sketch b on Fig. 5, or by freak fittings of unknown effect. 

With the arrangement ^^a" the 2-in. pipe leading upward 
would be grossly disproportionate for the requirement, when we 
consider the greater head available, and the decreased velocity. 
Fitted up in style " b, " the extra turns on the main riser still give 
too much capacity for the upper floors, creating a greater velocity 
than necessary for conveying the heat, and thus putting the 
branch under a disadvantage, unless throttling devices are relied 
upon. Form '^ c, " with the sizes proportioned with due consider- 
ation for the heads available at the main and the branch, will 



THEORY OF THE FLOW 21 

give the required capacity without adjustment, with less fittings, 
less pipe, less heat loss and less expense for labor. In cases 
where the main cannot be reduced and the resistance in the 
branch must be kept down, Y fittings as shown by the arrange- 
ment ^"d" are indicated. With an ordinary T as shown in "a'' 
the head available for such a branch would be further reduced 
and would become uncertain, especially when handicapped still 
more by excessive flow to the stories above. 

Total Head. — The sum of losses in head by friction, resistance 
and motion, Hf + Hj. + H^ = H enters in nearly every case into 
the calculation of conduits. 

For a simple pipe line with free discharge on one end, the total 
head gives the pressure or height of water column necessary for 
the desired delivery, or if the total head H is the known quantity, 
the difference between it and the combined friction and resist- 
ance heads H^ = H— (Hf + Hj.) will give the velocity head or net 
pressure available for discharge. The chart gives immediately 
the corresponding velocity and volume of water for the pipe size 
on which the losses of head (Hf + Hj.) are based. 

For an open distributing system, when H is uniform for all 
points of delivery, it must be determined as a basis for calculat- 
ing the several branches, which should be equalized, or propor 
tioned so as to make up the same total loss when discharging the 
desired amounts. 

In the case of gravity circulating H is given by the relative 
levels of heating and cooling surfaces, and the differences of 
temperature to be maintained. This available head is to be 
figured for each circuit, so that the sum of resistances can be 
made to balance it by selection of the proper pipe sizes and forms 
of local obstruction. 

With forced circulation, usually a closed distributing system, 
the total head is sought for equalizing distribution as well as for 
determining the proportions of the pump for propelling the water, 
and for estimating the motive power. The loss of head by 
friction, eddies, internal leakage around the rim, or slip, and 
changes of velocity within the pump, are in reality a part of the 
total to be overcome. It would be impracticable to express 
these hydraulic losses in the pump as a function of the head to be 
produced by the wheel, since the latter depends upon the near- 
ness with which the theoretical requirements, that is, the correct 
relation of dynamic and static heads, can be approached by the 



22 THE FLOW OF WATER 

commercial article to be used. The pump must produce a total 
head including these internal losses. Its speed and efficiency 
under given conditions should be known by the manufacturer, 
and it is proper, therefore, to call for a certain volume to be 
moved against a certain head, which head should always be 
understood to include the sum of losses from the outlet of the 
casing to the point of delivery, plus that of the suction or the 
return pipe up to the inlet. In order to avoid undue losses through 
discrepancies between the sizes of mains and those of the ports, 
it is best to state the size of these mains, or the velocity at which 
the water is to enter and leave the pump, thereby defining also 
the dynamic head and its relation to the static head. 

For the common type of single stage centrifugal pump the 
peripheral speed will average about 1.15 V, or 15 per cent, in 
excess of the theoretical velocity corresponding to the total head 
outside the pump. The velocity at which the water should leave 
the wheel and the pump depends upon the relation of static and 
dynamic head desired, which is conveniently established by the 
charts. High static head or back-pressure against the flow and 
low velocity involve large area of outlet and call for a wheel with 
blades at a small angle to the tangent, imparting lower speed at 
higher pressure. High velocity and low back pressure would 
favor radial blades for which the discharge velocity at the rim 
may be nearly equal or even greater than the tip speed of the 
wheel. To what extent this velocity should be reduced in the 
casing or converted into pressure without excessive loss by cones 
at outlet and inlet connections to piping, would depend on 
commercial considerations. 

These general conditions should be recognized in order to 
assure a fair hydraulic efficiency for a circulating system, but 
the exact relations of theoretical velocity, tip speed and discharge 
velocity at rim and ports must naturally be governed by the 
commercial sizes available. As stated, the selection should 
finally be made by the manufacturer. 

Motive Power. — The power required to propel a given amount 
of water per hour through a system of conduits is equivalent to 
the work of lifting its weight up to a height balancing the total 
resistance to the flow, which the chart gives in feet of water 
column. In foot-pounds per second this will be 

WH ^ . ^ WH 

hence m h. p 



3600^ ' 3600X550 



THEORY OF THE FLOW 23 

This energy represents the net output required of a pump. 
The motive power necessary to drive the same must include its 
mechanical losses, also the internal hydraulic losses, all to be 
overcome by greater power delivered to the shaft. The losses of 
motion and leakage are to be made up by larger diameter, 1.1 to 
1.25 times the theoretical. This item alone will often increase 
the power need from l.P, up to 1.25^ of the theoretical, or from 
21 per cent, to 57 per cent, additional. The friction of wheel and 
casing, independently of the losses of motion, will require also 
from 33 per cent, to 67 per cent, extra power, according to perfec- 
tion in design and execution. The mechanical losses are a small 
percentage. The power delivered to the shaft will therefore 
have to be from 60 per cent, to 135 per cent, greater, for pump 
efficiencies varying between 67 per cent, and 42 per cent. Allowing 
for the uncertainties of the motors themselves, it is proper to 
purchase the motive power on the basis of 2 to 2 1/2 times the 
value obtained by the chart, as stated. Only for large units, 
specially designed, or well suited to conditions, is it safe to take 
less than twice the theoretical h. p. 



CHAPTER III 
FORCED HOT WATER HEATING. 

Chart I. — The chart for forced circulation is intended princi- 
pally for district heating from a central station, and wherever 
heat is to be transmitted by hot water at long distances, for 
which the flow must be created by mechanical means. 

When heat is conveyed by water, only a margin of the B. t. u. 
contained in the fluid is transmitted. Economy in operation 
will therefore demand a return circulation of the medium under 
a certain drop in temperature. This drop, as well as the mean 
temperature, depends upon the conditions under which the heat 
is absorbed and emitted, that is, upon the temperatures available 
for generating and the requirements as to intensity of the heat at 
points of delivery. Other things being equal, a higher flow 
temperature will permit transmission of the heat with smaller 
volumes, at a greater range, while lower flow temperature, with 
relatively warmer return, involves greater volumes. The drop 
in temperature, defining the quantity of water to be kept in 
motion, ranges between 10° F. and 30° F. in ordinary practice. 
The chart gives the heat transmitted per 1° difference. Thus, 
if 500,000 B. t. u. are to be translnitted with the water cooling 
off by 10° F., the weight of water circulated, will be 50,000 lb. per 
hour, or 16,667 lb. for 30° F. drop between flow and return. For 
a range of 20° F. the amount of heat transmitted can be read 
directly on the scale of gallons per minute, each gallon carrying in 
round numbers 10,000 B. t. u. per hour. 

The friction is given for a unit of 10 lin. ft. of standard wrought 
iron pipe, and the resistances for the ordinary types of fittings and 
apparatus, the losses of head being expressed in feet of water 
column. The necessary data is added for correcting the volume 
to allow for heat losses, and for correcting the head when influ- 
enced by temperature. 

The supplementary chart is intended for determining the 
theoretical velocity, area and power requirement, from the total 
head. A separate scale is given for conversion of the head in 

24 



fhe Flow of Wafer for Various Forms of Obsfrucf 



CHART I 

FORCED HOT WATER HEATING 

THROUGH STANDARD fl-EIGHT IRON PIPES 



Water circulated i 



„ , „. U.t.u. per tiour 
lb. per hour U = — . 

i .t.u. per hour 

05x(i0x((-(,)**^*' '^• 

i.ft. per sec. Q = =.00000463 IT ( 



gal. per ii 



Velocity of flow in cu.ft. per set 
Head in ft. to overcome fricti( 



3600 X 




of obstruction *, = 1.38r-r— . 
creae\eociy ,-— . 
Total head in ft. to be produced by pump H =Hf+Hr 

" pressure in lb. per sq.in. to be produced by pumpP = -^ff=.42H(200°F.) 
Horse-power to move water against total head = - 
Energj- in B.t.u. p.h. to n 



3600X650 
2M5 W.H. 

"3600x550 

Theoretical velocity giving total head of deliverj' V = v'2jff- 
Approximate peripheral velocity of pump wheel = 1 . 1 F to 1 .25 V. 



: .00128 W.H. 



Orifice in sq.ft. corresponding to tlu 



The 1 



1 S.|.ft. = l.M> 






, =20) , 



mittod .sliould include the heat lost in transit as far as 

affecting the volumes for the run to be figured. To estimate this loss for a 

mean temperature of about 200' F., t ake roughly for 

insulated pipes in conduits per sci.ft, of surface 60 B.t.u. per hour. 

" " buildings per sq.ft. of surface 100 B.t.u. per hour. 

bare pipes in conduits underground per sq.ft. of surface 150 B.t.u. per hour. 

" " " buildings per sq.ft. of surface 350 B.t.u. per hour. 

less the energ\' to overcome friction and obstruction in B.t.u. per hour. 



Corrections 
If the heat absorbing and emitting points are on different levels, the head 
to be produced by the pump should be corrected accordinj 
weight and height. For water at 200° F., H, =// ±.00037 (( -(,)/i (approxii 




Oischar^e of Wafer in 1000 lbs. per hour = lOOOBf.u- transmitfed pt 



difference ; also in gal. per minufs (approx 



Oischargt 



40 50 60 70 BO 90 I 

100 zoo 500 

of Wafer in lOOO Ib.per hn - lOOO B.t.u. fn 



1000 «.-^^.^...i/. / 

1.000 gal p.i 

1° fahr. difference 



FORCED HOT WATER HEATING 25 

feet of water column into the corresponding pressure in pounds 
per square inch. 

Distribution on a Circuit. — Since the flow of water to each indi- 
vidual radiator, coil or other appliance on a circuit must be gov- 
erned by the head available for it, which is the differential be- 
tween flow and return mains at respective junctions, it is evident, 
that the branches should be so proportioned that their resistance 
will equal this available head, when delivering the requisite 
volume. Between the back pressure in the flow system and the 
suction in the return there is a neutral zone in each branch cir- 
cuit to and from the individual heat emitting appliances. In a 
closed system these zones, or points where neither suction nor 
excess pressure maintains, are simply under the head due to the 
w^ater column above, which is balanced and does not bear on the 
flow. Hence the total difference of pressure, or loss of head, 





ten 


f,^ 


ib , 


c 




■ ; 




1 

A 

J 


I 








~C^ 




K'Pump 


1 




\" 




W, 


% 




C/ 



Fig. 6. — Schedule of forced hot water heating. 

must be the same between the pump and any of the neutral 
points on the branches of delivery. It follows, also, that the head 
lost between two opposite junctions of flow and return mains 
must be the same through any of the individual connections. 
The idea is illustrated by Fig. 6, wherein the loss for the run 
from a to a^ is equal to the total for the run a-b-b^-a^ and the 
total for a-b-c-c^-b^-a^. Appliances nearer to the pump will 
therefore have a greater head available for the flow through their 
individual branches, and should be proportioned accordingly. 
For instance, the differential head between a and a^ is greater 
than that between b and b^. If sized for the same head, there 
will be an excessive delivery through a-a^, or a partial short 
circuit. Under a constant head, this will mean a shortage for 
other branches toward the far end of the line. In other words, 
there will be uneven distribution, or, when adjusted by throttling, 
it will be distributed at a disadvantage, with pipes larger than 
necessary in some parts, and probably scant diameter in others, 
involving more friction. A pipe system that is adjusted by trial 
after installation is likely to cost more and to require more power, 



26 THE FLOW OF WATER 

thus increasing both the investment and expense of operation. 
Distributing lines designed to equalize the loss of head as nearly 
as is possible with the commercial sizes will be the most econom- 
ical and may be relied upon to give the desired delivery. That 
the theoretical requirements can be closely approached by stand- 
ard piping will be shown in application of Chart I. 

To equalize the losses of head for the same total presupposes a 
fairly accurate estimate of the quantities of water to be carried 
in all parts of the conduit system. These quantities are not 
always proportional to the amount of heat to be delivered at 
certain appliances, but are often materially increased by the heat 
losses in transit. If we consider the latter as part of the heat to 
be carried, the volume of water to be moved increases at the same 
ratio. 

As a general rule, the heat emission along the pipe lines should 
be estimated for all branches and for such portions of mains in 
which they would be a material item. This is usually done on 
hand of a schedule of tentative sizes, as will be outlined by the 
example to follow. When such losses occur in conduits branch- 
ing into two or more individual lines, the latter must handle their 
proportionate shares of the excess allowed for the heat losses on 
the main. If the losses in the mains are relatively small, and 
partially offset by the heat developed through friction, it is proper 
to disregard the mains, inasmuch as the mean temperature and 
heat delivery can be kept up by a slightly greater range, without 
appreciable effects on the heat distribution. 

Effect of Throttling. — A system of conduits should be designed 
for the maximum delivery and equalized with all branches carry- 
ing the full volume. Even then the distribution will be imperfect 
when any part of the system is shut off. The degree to which the 
discharge through the remaining outlets is affected depends upon 
the design and proportions of the conduits, also to an extent upon 
whether the speed of the pump or the power are under control. 

If the power put into the flow is constant, the product WxH 
must remain the same. Thus, with the amount of water reduced 
by throttling, the total head is increased, and to a lesser extent 
also the delivery to the other branches. The pump will speed up 
automatically to produce this additional pressure, unless con- 
trolled to prevent it. 

Under constant pump speed the total head H will remain 
practically the same with throttled discharge. It is effected 



FORCED HOT WATER HEATING 



27 



only in so far as the pump efficiency may vary under throttling. 
The volume in the main is naturally reduced according to the 
branches shut off, and therefore also the pressure losses along 
the line, which will leave a greater balance for the open branches 
in which the flow is increased. This increase, however, is not 
proportional to the extra pressure available, but only about to 
the square root of the same. Hence there will be a reduction in 
the total volume delivered. The power need at constant speed 
therefore decreases with the output or the product WH. The 
energy saved depends upon the efficiency of pump and motor 
under changing load. 



<I4900> 
[31700] 

^ ^ r~\ 

30000 - (9.85^ 



B-^ 





Z50Ft. 





1 1 W-innnnn Vo ri\ 



V 300000 ^ ^ 
(295500) (7.75) (8.0) 
[297500] [7.85] [8.05] 
<I42000><1.95><2.0> 
Pump 



^ 



w 



(8.6) 
[8.55] 
<2.I5> 



'I0«30000 

WHi[|0.| .29750] 
.<2.5M4200> 



250000 

(273700) 

[244500] 

<II7500> 
Bfu ru 1 1 speed 
( ) wiihAshutoFr 
[ ] wifhB shut OFF 
< > '/z speed 
t-f, -- IO°F. 

M/ - ^^-^ 



iiorV/i) 



210000 
(230200) 
[201000] 
<98000> 



180000' 
197500) 
20 10 00] 
<83500> 



Fig. 7. — Example of forced hot water heating system showing effect on distribution of 
throttling and speed reduction. 



Fig. 7 may serve as illustration of the effect of reduced volume 
on distribution. It is assumed that the pump speed is not under 
control and that the power put into the flow is constant. When 
the first br0,nch A is shut off, it will be noted that the total 
delivery as marked in parenthesis (295,500) is smaller, and the 
total head (10.15) larger than with the last branch B cut off, 
for which case the figures are given in brackets [297,500] and 
[10.1]. If the volumes are calculated at which equalization will 
take place, it will appear that in the first case the excess volume 



28 THE FLOW OF WATER 

is about equally distributed through the balance of the system, 
while the throttling at B gives an appreciably greater increase to 
the nearest outlet ahead of it. It becomes evident also, that 
with relatively small pressure losses in the main, the total 
volumes and the distribution are less affected by the throttling 
of discharge outlets. In this particular instance, the main, if 
proportioned simply according to the volume carried (or W 
instead of WxH) would be reduced to 2 1/2 in. for 210,000 
B. t. u. This would make equalization more difficult with all 
outlets in use and would shunt practically the whole excess 
volume under curtailed discharge through the branches at the 
near end. Larger mains permit the initial pressure to be kept 
up well to the far end of the line and assure delivery under a 
greater variety of conditions. The velocity head as an element 
of uncertainty in distribution is at the same time kept down, and 
the trunk line approaches the idea of a reserve tank or plenum 
with perfect equalization. 

Aside from the questions of power, first cost and heat losses, 
the sizing of a main, should, for these reasons, be governed by 
the relative importance of equal distribution. The extent to 
which delivery is to be throttled, and future outlets to be pro- 
vided for should also enter into consideration. 

Distribution under Reduced Head. — The bearing on distribu- 
tion of a reduced total head, through slowing down the pump, is 
very slight. The volumes discharged through small branches are 
decreased somewhat more than those flowing through the larger 
ones, as shown again on Fig. 7, by the B. t. u. and losses of head 
given for half speed. This fact is due to the relatively greater 
head required for the flow in small pipes at low velocities. This 
will be true of course, only while the velocities are still above the 
critical stage below which the coefficient of friction is much 
reduced. Under ordinary conditions, the total delivery is less 
than that proportional to the speed of the pump. At half speed 
as shown, the discharge will be smaller than .5W, while the head 
created by the pumps cannot exceed .5^H, unless through 
chance or poor selection its efficiency is improved under light 
load. The theoretical power decreases also as the volume, and 
is therefore smaller than .5WX.5^H, being a function of 
.o^X W.H, assuming that the pump efficiency remains the same. 
If the latter decreases materially at lower speed, the actual 
power is liable to vary less than the cube of delivery. The 



FORCED HOT WATER HEATING 29 

example on Fig. 7 indicates, through the < B. t. u. > calculated 
for half speed, that in ordinary practice the effect on distribution 
of slowing down or speeding up is negligible. The reductions in 
the volume, how^ever, will be appreciably below the proportionate 
speed, especially when the effective total head is further decreased 
by lower pump efficiency. This fact should be borne in mind 
when speed reduction is to meet a stated requirement. 

Heat Developed by the Flow. — When determining the heat 
losses in transit, it will pay in some cases to figure out and deduct 
the heat developed by the friction of the water in the pipes. 
This item may, under extreme conditions, result in higher tem- 
peratures at the far end of the flow main. The emission on the 
run remains practically the same, but the heat thus supplied, or 
returned to the system, reduces the necessary allowance in vol- 
ume to make up for the losses in transit, especially for the mains, 
in which the heat losses are relatively smaller, while the friction 
is usually greater. This heat is the thermal equivalent of the 
mechanical power imparted to the water, and converted, as 
resistances are overcome along the pipe line. Expressed in 

B. t. u. per hour it is= '- = .00128 W. H. Strictly 

^ 3600X550 ^ 

taken, this heat should be figured for each section of conduit, sub- 
tracted from the losses by convection, which can be estimated, 
but for practical purposes it will suffice to establish the total, 
and its probable effect on the temperature of the flow. The 
value for H in this formula represents the sum of friction and 
resistance heads and should not include the dynamic head 
maintained. The latter manifests itself as vis-viva or mechanical 
power, until the pump is stopped, when the momentum of the 
flow is gradually lost in friction and only then converted into 
heat. It should include, however, the hydraulic losses in the 
pump, which can be estimated from its efficiency. 

Taking for instance a tax on a system of 6,000,000 B. t. u. to be 
transmitted at 20° F. differential, and requiring 300,000 lb. of 
water per hour or 600 gal. per min., we find that this volume 
flowing through a 6-in. main at a temperature of 200° F., will 
lose about 8650 B. t. u. per hour by convection per 100 ft. run 
through an insulated pipe in a conduit. The resistance for that 
length, including four elbows, two right angle tees, and two gate 
valves, will take a head of about 7 ft. Hence the energy ex- 
pended to overcome it would be .00128 X 300,000 X 7 = 2700B. t. u. 



30 THE FLOW OF WATER 

per hour. This heat may be increased by other local resistances 

upstream, such as a coil, and will benefit more or less by the 

friction head of the pump, which generally doubles H, so that a 

moderate increase of speed, or better protection from heat loss, 

might easily bring the B. t. u. generated up to the heat losses in 

transit. The latter is therefore, most likely to become negligible 

as an item affecting the volume or the temperature. Inasmuch 

as the heat loss by convection along the mains is relatively 

smaller, while the resistance is relatively greater than that in 

branches, it seems quite proper under similar conditions to make 

no allowance to the volume of water to cover the heat losses 

in mains. 

Temperature Head. — If the heat absorbing and emitting points 

are at different levels, the pressure to be exerted by the pump 

may be modified appreciably. Such differences of level between 

boiler and radiator will create a certain head, due to the unequal 

weight of the two water columns represented by the flow and 

return mains. This temperature head is proportional to the 

difference in weight per cubic foot and to the height of the col- 

w^-w 
umns and can be expressed by h^ = h , or by the variation m 

W + Wi 

density for 1° F., which is also the coefficient of expansion. At 
about 200° F. h^ = . 00037 (t-tjh (approximate). If heat is 
delivered at a higher level, the head due to differences in tempera- 
ture will naturally accelerate the flow, unless it is discounted or 
subtracted from that produced by the pump. The reverse will 
take place when the heater is elevated above the cooling surfaces, 
in which case the temperature head is negative and must be 
added as a loss to the total to be overcome by mechanical means. 
The corrected head may be expressed therefore as 

He = H±.00037(t-tOh 

For transmission of heat at long distance, such differences in 
level have little bearing on the hydraulic slope, and on the flow 
of the water, the temperature head being only a small fraction 
of the total required to overcome the high resistances conditional- 
in such cases. For individual heating apparatus where forced 

circulation is used mainly to accelerate, the ratio — will be 

materially affected, especially with greater range of tempera- 



FORCED HOT WATER HEATING 31 

tures. The corrected heads must be appHed, of course, to each 
branch individually, when determining its size. Where the 
temperature range is varied according to weather, such a system 
should be balanced for average conditions and proportioned so 
that the extra head due to highest flow temperature will not 
materially affect distribution. 

Static Head in a Forced Circuit. — In a forced circuit of a given 
height of water column (see Fig. 7) represented by the elevation 
of the expansion tank above the pump, there is a limit to the 
pressure difference that can be maintained by the pump. If 
the suction at the inlet overbalances this natural static head, 
Hg which would maintain at the state of rest, there will be an 
actual vacuum at that point. This vacuum will lower the boiling 
temperature of the water and may thereby generate steam at the 
pump suction, thus interrupting the circuit. When there is any 
danger of such occurrence, the tank level should be raised, or 
the resistances eased. In locating the tank it is best to place 
it at some neutral point along the circuit, or provide a neutral 
point by properly sized flow and return pipes to and from the 
tank. These pipes should present the same resistance to the 
flow as all other branch circuits when passing a sufficient amount 
of water to make up for the heat loss in tank and connections, 
thus preventing a short circuit near the pump. 

Application of Chart I. — In order to apply the theories out- 
lined, it is essential, in the beginning, to establish all the factors 
that may bear on a problem. The methodical way to do this 
is to present the situation graphically, giving a comprehensive 
view of the apparatus to be calculated. This may be obtained 
simply by a tracing or print of a plan of conduits, with elevations 
worked 'into it and special features noted. It should provide 
a schedule of lengths and heights to scale, show all items of 
local resistance, and permit the quantities carried to be 
marked down for all parts of a circuit. These quantities, in 
B. t. u. per hour or in gallons per minute, should be stated for 
each section of main and branch carrying a constant volume or 
weight, the total for all the branches making up the tax on the 
pump. 

On the basis of these quantities the system may then be sized 
tentatively for an even rate of pressure loss. The initial velocity 
in the main is assumed as experience may dictate, according to 
the power available, length, or other features. Assuming for 



32 THE FLOW OF WATER 

instance a velocity of 7 ft. per second to carry 24,000,000 B. t. u. 
at 20° F. drop, or 2400 gal. per minute in a 12-in. pipe, the loss 
of head by friction will take place, according to chart I, at the 
rate of .15 ft. per 10 lin. ft. of length. The proportionate sizes 
for decreasing quantities, as branches are taken off, may then be 
found quickly along the same horizontal line of friction head. 
Thus a portion of main carrying 5,000,000 B. t. u. or 500 gal. 
would call for a 7-in. pipe as the nearest commercial size, giving a 
velocity of 4.2 ft. per second. For 40,000 B. t. u. it will be a 1-in. 
pipe, at about 1.5 ft. velocity. This method of proportioning 
gives a rational way of reducing speed for smaller sizes and per- 
mits a preliminary estimate of the total loss, which it may be 
necessary to keep down or to increase for various reasons. In the 
former case it is proper to choose a line of lower friction head by 
which to proportion the mains, or vice versa. 

From these preliminary sizes the heat losses in transit should 
be estimated and added to the quantities. As stated, it is usually 
sufficient to allow for the losses in branches and bare portions of 
mains, but it must be remembered, that the increased volume for 
a branch must pass also through the mains, and through any 
further branches beyond. 

When all quantities have been corrected, and allowance made 
for any temperature head, the final calculation of sizes with a 
view to equalizing can proceed on a safe basis. Starting at 
the pump, the losses of head by friction and local resistances, 
as derived from the chart are added together for the first sec- 
tion carrying the full volume up to the nearest branch. The 
same is marked on the schedule, just ahead of the junctions on 
flow and return mains. In using the chart, it is convenient to 
figure first the friction head for the length in question. This 
gives the velocity line along which the resistance head for el- 
bows, T's, and other items of obstruction may be read. The pro- 
cess is repeated for the runs of mains to the next set of branches, 
and the sum of these being added to the first figure. The total at 
the last pair of junctions, plus the resistance of the branches and 
the appliance furthest from the pump will give the total pressure 
head for which all other branches nearer to the pump should be 
equalized. 

The process of equalization is necessarily tentative, but with 
some practice and judgment in assuming the sizes, it will be 
found that one or two trials will suffice to find the nearest com- 



FORCED HOT WATER HEATING 33 

mercial diameter, or combination of diameters, that will produce 
the desired resistance. As stated previously, there are various 
means of bridging the wide gaps in capacity between standard 
sizes. As a matter of fact, equalization may be carried to any degree 
of accuracy that may be desired. No valid objection can be 
raised to the use of different sizes for flow and return pipes, nor to 
changes in the diameter for any length desired. In such cases 
the items of head are simply obtained on two different velocity 
lines for the same volume. Frequently, the length of branches 
may be varied, or the flow and return mains looped in opposite di- 
rection. Practice will teach the best means for various situations. 

The total head for a system, as determined for purposes of 
equalization gives also the data for sizing the pump and motor on 
hand of the auxiliary chart. The intersection of the line for 
the total head with that for the total volume carried, gives both 
the theoretical horse power and the equivalent orifice. The 
corresponding velocity is found at the intersection of the pressure 
line with that of theoretical velocity. The application of this 
data is explained in the general chapter on the flow of water. 

Example. — The example presented by Fig. 8 shows a portion of 
a district heating system, with underground flow and return 
mains, insulated and laid in conduits. The water is set in motion 
by a centrifugal pump, heated by steam coils in a large drum 
through a range of 20° F. and conveyed to different appliances. 
Each of these is absorbing the heat through coils of pipe arranged 
in continuous circuits, as a part of the pipe system, or as a sub- 
sidiary individual heating plant, controlled by valves. The 
length and sizes of these coils, as far as they bear on friction and 
resistance, are stated on the schedule. The quantities are 
marked in B. t. u. per hour for each sectional run and the head is 
figured for each set of junctions. The flow and return mains 
being parallel throughout, it can be assumed that they present 
the same resistance since the slight reduction of velocity and 
friction in the return system due to the shrinkage is a very 
small item. The odd resistances of the apparatus near the cir- 
culating pump are figured separately. They include the item 
for a Venturi meter, for which a coefficient of resistance of .1, 
based on the throat velocity, has been assumed for safety, with a 
liberal allowance for friction. The losses of head for the heater 
and pump connections are added and set down as initial head for 
the mains. The figures given at the successive junctions accord- 

3 



34 



THE FLOW OF WATER 




FORCED HOT WATER HEATING 35 

ingly give the combined losses up to these points. The differen- 
tial between these junctions must make up the total pressure 
exerted by the pump and govern the delivery for each unit on the 
circuit. The sizes of individual connections are relatively greater 
as the available pressure- becomes smaller near the end of the 
run. This is specially noticeable at the first branch, supplying 
a small building at very long distance from the main. The 
excess of head at that point is fully 45 ft. and permits a surpris- 
ingly small connection, considering its length. On account of 
the long run of this branch the heat loss in transit is added to the 
tax, so that it will in reality receive more water in proportion to 
the B. t. u. to be delivered at the end. The branch has been 
kept somewhat larger than it figures, but the excess of water 
due to that cause is so small that it would hardly affect the 
delivery to the other appliances. 

The differences in level do not exceed 50 ft. in either direction. 
The effect on the flow for a run of 1500 ft. accordingly figures 
.00037X20X50 = .37 ft. or less than 1/2 per cent, of the total, 
and is therefore a negligible quantity. 

The correction to the volume for heat loss in transit is also 
very small, since the heat developed by friction practically 
offsets the former. At full speed the drop in temperature near 
the extreme ends is, in fact, barely perceptible according to actual 
readings. 

With the exception of the first branch, already mentioned, the 
equalization is carried out to within about 5 per cent, of the total 
head. The discrepancies between individual branches are rela- 
tively greater, but the excesses and deficiencies of volume due 
to these faults in equalization are of necessity smaller again, and 
the effect on the heat delivered is still less. At any rate, the 
calculation is within the limits of error in sizing up the factors 
and arising from the uncertainties of execution. 

The total head to be created by the pump may safely be taken 
as equal to the average calculated for the branches, in this case 
about 91 ft. or a pressure of 38 lb. per sq. in. According to 
the auxiliary chart this corresponds to a theoretical velocity of 77 
ft. per sec. an orifice of .014 sq. ft. and ports of .15 sq. ft. area. 
The peripheral speed of the pump wheel should be between 85 
ft. and 90 ft. per sec. and the blades curved to a small angle 
with the tangent to convert this motion into pressure as far as 
practicable. The sizes of the ports need not necessarily cor- 



36 THE FLOW OF WATER 

respond with those of the circulating mains. In fact, a hydrau- 
lically more advantageous arrangement is made with a pump 
having small outlets, say 5 in. diameter, connected to the 6 in. 
mains by easy taper pieces. 

The power to overcome friction and resistances in this in- 
stance figures 11 h. p. by chart. The motive power provided is 
about 22 h. p. This assumes an efficiency of 50 per cent. 



CHART II 

HOT WATER HEATINQ BY GRAVITY 



THROUGH STANDARD WEIGHT IRON PIPES 



ii/=.0267— -Xji5j. 



Effective height, or actual heiglit and equal to cH -jj::^ U 

mth water column, at 200" F. and 160° F. ^" -^o^^^n" -''O-^" 
or cff =difference in Il\c1 !.rtT,Tpn lir:if rccci\'ing OJid emitting surfaces. 

affecting llie vuliiim ^ fm il.r run- in he figured. To eatimate this loss talte 
roughly for 



The range of 40° F. i 



. anil ;. by l.U at about ISO'l 



.1 


f 5 




/tppr 


oximate P 


;,,= 5->e3 /!«./ 


med ef B.tu. 
60 70 go 30 


per hou 


■ -H% Allovrance far Eyery ft of Pipe Length 


JOOO 1000 5000 6.000.000 






















y\\ 




/ 




/ 


/ 






/ 




■^ 


/\ F" 














• 






/ 




/ 






/ 




/ 






y 




















,' 


/ 




/ 






/ 4 




/ 


/ 


























/ 


/ 






/ 


/ iin^riiii 


/ 


<W' 




^ 




;: 






















/ 




/ 




/ 


L ' . L^ 


J^4^ 


^ 




?^ 


5^? 


Z-^ 




"T- 












7 
/ 


/ 


/ 




/ 


/ 


/ 


nr'X-^ 


i'-i-:i 






^ 






: 














»^^ 
y 


/ 


/ 






1^ 




^^5 


2:::^^^': 




^ 


:2 








= 








. 


$• 






( 






p- 


iii 


ii 


^ 


i 


g 


/, 


Ill 


i 


5 




§Hii 




--7^ 


^ 


^ 


^k--% 




^ 






1 


l^i 


lii 








.,- ■ "XU; 




/^ 




^ 






^"-^ 






■ 


^ 


;2 /! 


1 4-T U 




^iJ^T^/ 


/ 


V -^^ 


fJ^ 






- "' TH 






' / 








■ — "ii^ 




C^"^ 




-;?fCW11^JJ 


■4J^' / 


/ 


/ 


^ ^^, 


zn. 


^ 




- - /' ' 1 


, — -;>' 




■^-^ 








"^^--^ 




^ 




^ 


/^?rJQ^w^ 


/ . 


' / 


// 


V^'^-/- 






'^" 






e^ 


C-^ 






v^^ 


v^ 




M 


?i/'^ 


:3^...: . 


/ / /. 


V 


/ 


2^-^-/3 


-- 




?;-:-:; 




zi^ 


[^ 


/ 


"^"Z-""' 


\i"''/ 




'A 


¥ 




/ 


4//' 


/ / 


/. 




'/ 


%-/-- 


g 


mi 


=;:::':: 




'^ 


?1 


-^ 




'^'/W- 


^ 


/ 


/ 


f 




,Ay[\m 


^A 


/. 


"/ 


/ 


// 




? 


Z'-: 


;i---t; 


^^--' 


^ 


^ 




/ 


/ / 


y/// 


/ 


/>^:d/j 


^^^ 


/ 


^ 


i 


f^ 


'^^;:::: 






=5 


/ 


' / 

/ 
z - 




y 


/ 


/ 


/ 

2 






i 


/ 


/ 




EE"' 


^ 


7 


.^.. ... 




1^ 


;t 


30 ■, 5 


'^e w60,o 


b 


b 


z 


/ 


S^z 


-7 -''; ■-■ 

00 / 


^ 


■^^ 


3000 WOO 3t 


s„ 



Emitted by Wafer from 200° fatir to 160° f 




£00" fahn to I60 fahr in 1000 B. i 



mo 3000 4000 5000 6,000,000 B t. 



CHAPTER IV 
HOT WATER HEATING BY GRAVITY. 

Charts II, III and IV. — Gravity circulation may be effected 
under widely different conditions. Hygiene demands liberal 
heating surfaces, at temperatures considerably below the boiling- 
point, while economy tends in the opposite direction, toward 
smaller surfaces and piping. Aside from structural reasons 
that may also enter into the problem, the relative importance of 
those two points will decide whether an apparatus should be 
designed to meet the extreme tax at moderate temperature, or 
whether it be permissible to depend on greater intensity of 
heat, and a greater drop, in order to reduce the expense. The 
diagrams Nos. II and IV may be said to be within the limits 
of good practice in either direction. It will not pay, except 
in special cases, to figure on lower flow temperatures than 180° F., 
on account of the rapidly increasing heating surface, nor on a 
smaller drop than 30° F., since the bulk of water becomes too 
great and takes too much time for reheating. To use a greater 
range than 40 degrees at 200° F. flow temperature, will make 
the piping undesirably small in some places, and involves closer 
calculation. The third diagram represents average practice. 
The choice in each case is determined in general, as stated, by 
considerations of hygiene and economy, but is also influenced by 
structural conditions and the necessity of quick reheating. 

Closed systems, for medium and high pressures, which owe 
their earlier development to the facility of forcing, are gradually 
becoming obsolete in the same measure as the means of obtaining 
perfect circulation, under all sorts of conditions, with an open 
system at low temperatures are better known and appreciated. 
For this reason no diagrams have been worked out to fit their 
case. A closed system can be calculated, if need be, on hand 
of the present charts with proper application of corrections. 

For apparatus which depends on artificial devices for ac- 
celerating the circulation by steam or other fluids of lesser density 
in one form or another, special charts might be worked out to 

37 



38 



THE FLOW OF WATER 



cover the theories in question. In view of their limited field 
of legitimate use and on account of the great variety of systems 
and schemes, each presenting a different problem, no attempt 
has been made to cover these special cases. They are appli- 
cations of the same general principles and a study of the forces 
active in natural circulation gives the best means, and is neces- 
sary in fact, for planning artificial circulation to best advantage. 
Balanced Gravity Circulation. — It is assumed that the heating 
requirements to be met by the different appliances, radiators or 
coils have been determined, and that these heat emitting surfaces 
are disposed so that they will deliver the thermal units as in- 
tended. The problem will then be to distribute the heat carrier 
accordingly. In individual plants sufficent power is usually 











~ r~ 


'-^ 





— 












c, 












h, 


'W 


-w. 












-w 


w, 1 


,c 




e. 








1 


-TF" ~ 


-^^4 




1 


,d 


-w, 


r 


1 


:b, 1 


1 


/f, 


k 


■w, h 




hz 






— 


- 


_ i_ 





>_ 








L. 


— 







Fig. 9. — Schedule of hot water heating system with underfeed mains. 



created for moving the required amount of water by the act of 
warming, through which a very small portion of the heat applied 
is liberated as live force in expanding the fluid. This hydro- 
motive force is given by the differential weight between the warmer 
and cooler columns, usually designated as flow and return. It 
is dependent on temperature difference and on the height be- 
tween the mean levels of heat absorbing and emitting surfaces, as 
expressed by h(wi-w), using the designations on Fig. 9. 

At even distribution to each unit, suited to its cooling capacity, 
and without heat losses in transit, the differential density 
w^-w will be the same throughout a system. The height h 
on the other hand, will differ, being given for each radiating 
unit by its level above the boiler/ which level can be varied only 



w 
h3 



T.3 

E: 

- 

01 !> 

bll 

lo 






I 



Approximate Pipe Sizes A' 



CHART III 

HOT WATER HEATING BY GRAVITY 

190° F. to 155° F. 
THEOUGH STANDARD WEIGHT IRON PIPES 
Weight of water cireulated in lbs. per hour W — '^'^l ' 
Veloeilyof«owmtt.persec..- JITST'SBOOX 60.70xa '" ' 



J head in ft. required H = H,-\-H,. 



ilive height, or actual height and equal XxteH = ^ ^ II 
I required "' "' 

. -. ^ „ 60.70 



" horizontal pipea per sq.ft. of surface 320 I 
Corrections 
The rangp of So" F ma\ be considered that between 



!e\elofheatemittingf.urface>tst!il h'llp! Tin i 



Fof(-( 2')T I 




Meat Eimifted by Wafer From IQC^f^ahn to ISS'tah 



Heat Emiffed by Wafer from /90°rahr. to ISS^fahr. in !000 B.i 



HOT WATER HEATING BY GRAVITY 39 

by raising or lowering the boiler and radiation, which is not 
practicable as a rule. With equal temperatures in the several 
columns of one system, it is the height, therefore, which deter- 
mines the pressure available for creating the flow. This actual 
height, or the corresponding pressure, must be equal to the 
pressure required to overcome the combined losses by friction and 
local resistances Hf + Hj. = H for the entire circuit bounded by the 
respective appliances. Since the mean density of the water for 

W + Wj 

the circuit is , the pressure to be balanced by h(wi-w) is 

W + Wj 

equal to — - — H. This is in substance the fundamental equation 
used by RietscheP and quoted in all standard books for calcu- 

W + Wi 

2 

lating gravity circulation. It gives the value for h = H, 

Wj— w 

which is the actual height of the water column required to pro- 
duce the flow, under a certain drop in temperature. It is iden- 
tical with what is usually called the effective height eH, and must 
be equal to the height available between mean levels of heat emit- 
ting and absorbing surfaces. 

Distribution of the water to a number of appliances on 
different levels, and with varying lengths of piping, will hinge 
therefore upon the adjustment of the total loss of head along 
each circuit completed by an individual branch, to the pressure 
available for the respective points of delivery as given by the levels 
of the same relative to the heater. The pressure losses for the 
runs a-b-B-b^-a^, or a-b-c-C-Ci-di-bj^-a^ or a-b-c-d-e-E-e^- 
d^-b^-a^ in Fig. 9 should therefore be made equal to the differ- 
ential pressures created by the rising and falling columns of the 
heights h, h^ and h^, respectively. The principle may be 
followed with any scheme of piping, any number of branches, 
and for any distance and height, there being always a complete 
circuit traceable for each individual appliance. 

The volumes of water governing the pressure losses in the 
mains are those actually carried by the respective runs, and 
the total up to any junction is a part of the sum identical for 
all branches beyond. The losses of head in the mains, therefore, 

^ "Theorie und Praxis der Bestimmung der Rohrweiten fur Warmwasser- 
heizung." H. Rietschel. 



40 THE FLOW OF WATER 

must always leave a margin of head available for the branches to 

XT 

the appliance having the least slope -~, and the branches to 

those at higher levels or with shorter runs, must use up the 
surplus head, whatever it may be, by the resistances in rising 
lines and connections. Instead of equalization for the same 
total head as in the case of a forced system the ^problem is to 
balance, the unequal weights by conforming the resistance to 
the varying heights. 

It might seem, that with an available head exceeding that 
required, each branch will obtain at least its share of the water. 
This would be true, if all branches were run separately, to and 
from the boiler. With a collective main, however, the total 
losses of head for the several branches on a main are inter- 
dependent. An excessive volume flowing through one branch 
will necessarily also increase the friction in the main and reduce 
the balance of head available for some other branch further 
along. If this branch supplies a radiator on a lower level, it 
may easily happen that no head is left for the same. The water 
will not circulate through such a branch until the differential 
weight, increased through cooling, will establish the balance 
again, but for a reduced flow, and reduced mean temperature 
at delivery. 

Effects of Throttling. — The facility for central regulation 
which is peculiar to hot water heat, and is increased in range 
through accurate balance, eliminates to an extent the frequent 
necessity for shutting off individual radiating units. A pipe 
system should nevertheless be designed with a view to main- 
taining an equable distribution under such variations as are 
liable to occur through the temporary closing of appliances. 
The varying heads for the individual radiating units will natu- 
rally bear on distribution with curtailed delivery. 

In order to compare the effect with that obtained under an 
even total head created mechanically, the example illustrated by 
Fig. 10 is chosen to represent the identical case of Fig. 7, but 
without the extra length of main which calls for the forced flow 
in the former instance. It is assumed also that the range of 
temperatures is from 180° F. to 150° F., instead of only 10° F. 
The head required for each radiating unit, when receiving its 
share of water, is marked thereon. The approximation to the 
head available is carried close enough to give the assurance 



HOT WATER HEATING BY GRAVITY 



41 



that the actual volumes and temperatures can deviate only by 
small fractions from those desired. The effect of shutting off 
the first branch A is shown again by the B. t. u. in parenthesis, 
( ) . It will be seen that on account of the partial self-regulating 
tendency of gravity systems, the increase of volume for the 
other branches is not nearly as great as with the forced system. 
The reason for this lies in the decrease of the differential weight 
w^ — w due to the excess volume of water passing through the 
branches left open. This decrease tends to reduce the effective 
head at the same ratio for radiators at any elevation, but the 



B.tu 
( ) 
[ ] 



!- 




fullc3pacify,f-fr30 
wtfhAshutoff 
Y^ifhBshufoFF 
'/zcapacify f-f.-IS" 



(Z72000) (42) (51) (Z51600) 

[Z75000] [4.3] [50] [ZZ4400] 

<48> (5.6) (125000) 



I83400J 
;89900> 



Fig. 10. 



-Example of hot water heating system showing effect on distribution of throttling 
and reduced capacity. 



diminished friction head in the main leaves a proportionately 
greater height available for the flow to radiators on a lower 
level. The latter will therefore receive most of the excess 
volume, irrespective of the location of the branch cut off. This 
fact is confirmed by the figures in brackets, [ ], which give the 
B. t. u. with B shut off. We find for that case also a slightly 
greater excess for the branches ahead of B. The example 
shows, that with 10 per cent, of the heating surface shut off, 
the delivery to other appliances increases in no case more than 
3 per cent., and the variation between them is less than 2 per 
cent. While other cases, with relatively smaller mains and 
larger risers, would not fare as well, it is evident, that distribu- 
tion is not materially upset by throttling a considerable portion 
of the radiators, if a pipe system is properly balanced. 

Distribution at Reduced Capacity. — At reduced load, that is, 
with lower flow temperature as should be carried to suit the 



42 THE FLOW OF WATER 

weather, but with all appliances in use, the balance of a system 
is not fully maintained in theory. The mean water temperature 
at which, say one-half of the heat emission at 165° F. will take 
place is about 120° F. The drop in temperature, with the full 
volume passing through, would then be only 15° F. With the 
differential Aveight and the available pressure (wi — w)h thus 
reduced, the velocity will also diminish and bring the range of 
temperature up to an intermediate point, which can be found 
by tentative calculation. When the head available checks 
with the head required, the latter will give the velocity of the 
flow and the heat deliverable at each appliance, under these 
conditions. 

These amounts of heat delivered are figured up individually 
for the same example. It will be seen that the deviations from 
the desired quantity, that is, from 1/2 B. t. u., are relatively 
small, and have practically no effect on the rate of heat emission. 
The variations as they appear are due again to the slight shifting 
of the friction losses, the smaller branches being somewhat under 
a disadvantage at reduced velocities. Conditions will be different 
again at very light load, as the velocities drop below the critical 
stage, which is reached first for the smallest diameters. 

Higher temperature at the top of a flow pipe, which is a 
sign of even flow, as taking place below the critical velocity, 
also the variations of the coefficient of friction due to tem- 
perature, may sometimes upset the balance slightly or tempo- 
rarily, but these phases, however they may affect distribution at 
very low temperatures, need hardly be considered. 

Application of Charts II, III and IV. — The three charts for 

gravity circulation are based on the assumption of uniform 

difference of temperature t-t^ between flow and return. The 

w + w^ 
calculation is thereby simplified by a fixed ratio of — - — , to 

w^ — w, and allows the charting of eH in place of h given on other 

charts. In other words, the losses of head by friction and ob- 

w-l-W]^ , . . 

struction are charted on a scale to w. — w which is 100.3 to 

2 ' 

1 for 180° F. to 150° F., 83.8 to 1 for 190° F. to 155° F., and 70.8 

to 1 for 200° F. to 160° F., thereby giving directly the height of 

the two water columns necessary at the stated temperature 

range for overcoming resistances to the flow. The means are thus 

provided for immediate comparison of the head required with 



CHART IV 

HOT WATER HEATING BY GRAVITY 

180' F. to 150° F. 
THROUGH STANDARD WEIGHT IRON PIPES 

Weight ot water eirmlaiid in \l: |nr li"ur H' - ' ' j_,^ ■ 

ir W 

Velodty of Sow m ft. per *«■. >■ - ^-;,,-^„,_ "jgoo ^eO.S? xa '°' "■" 
3600-^0 

Head in ft. to overcome frietion A/ = .0257—- >^~njl- 



Total iiead in ft. required H =H 



f available 2 

Effective heiglit, or actual height \ and equal to cH = _ H, 
I required "' " ' 

with water columna at ISO" F. and 150- F. ^"- ....eT-LsT ^ -'°°-''"' 
or eH = difference in level between heat receiving and emitting surfaces. 



The B.t. 






the factois below 
ForI-I,=20'F.. 


nTultil 


IvbT'u a 


nd /, by 


,.o„at 


bout 105° mean fa 


24° 

30° 
32° 


l 


; 


': 


1 ,2.5 
1.15 

r.oo 


: ;: :; 




/so" fann in 1000 Btu per hour 



HOT WATER HEATING BY GRAVITY 43 

the actual height available for any circuit, which is a decided 
convenience and permits a better grasp of the problem in hand. 

In order to figure systematically, it is advisable to draw up a 
schedule of the entire piping as planned, showing horizontal and 
vertical distances to scale as illustrated by the examples to follow, 
and giving the tax on each branch and run of mains in B. t. u. 
per hour. Since the losses of head depend on the pipe sizes yet 
to be calculated, the latter must be assumed tentatively. This 
can be done by means of the charts for approximation which 
give the nearest commercial size for a given quantity in B. t. u., 
at any velocity, and the actual height necessary to overcome a 
uniform nominal resistance, assumed equal to that for a pipe 
length of 100 ft. The pipe schedule with heights and quantities 
can be sized directly from the diagonal lines representing about 
the mean level of the lowest surfaces, if a fair allowance is made 
at once for varying horizontal distances by adding about 1 
per cent, to the B. t. u. for each linear foot of pipe length from 
the boiler. For a radiator to emit say 12,000 B. t. u. located 
about 75 ft. away, at 20 ft. elevation, it is advised, for instance, 
to add 75 per cent. The approximate size of a connection may 
then be found at the intersection of the vertical line for 21,000 
B. t. u. with the line of equal resistance for 20 ft. elevation. 
For 30° F. differential, the next larger standard pipe will be 
11/4 in. For 40° F., it would be 1 in. diameter. The risers and 
mains may be sized in the same way, by estimating roughly the 
mean length of piping for the total to be carried and taking as 
height the elevation of the lowest radiator on the line. 

When the entire schedule is sized in this manner, the heat 
losses in transit should be estimated on hand of the data fur- 
nished. These losses are to be added to the tax in B. t. u. for 
the respective runs, to allow for an increased volume that will 
keep up the desired mean temperature. In so far as it emits 
heat, the distributing system should be considered as part of the 
delivering surface which defines the upper turning point, or 
mean level of cooling. If these losses in transit occur above 
or below the appliance, this level will be materially affected 
and call for certain corrections of the height in question, as will 
be further explained. 

The pipe schedule will then give the volumes carried in any 
part, the assumed sizes, the lengths and the local items of ob- 
struction, from which data all resistances can be figured accu- 



44 THE FLOW OF WATER 

rately by means of the other diagram. Starting at the boiler, the 
friction losses for each run between two junctions, and carrying 
the same volume, can be computed quickly from the scaled 
length, the chart giving the friction heads for 10 lin. ft. at the 
intersections of the lines for the B. t. u., and those of the as- 
sumed diameters. The several items of friction and local re- 
sistance for one section of constant diameter are found along 
the same velocity line and can be conveniently added up, the 
sum being noted at the junction. The total up to the next 
junction is added to the first, and so on successively, up to the 
points of delivery as will be illustrated by various examples. If 
flow and return pipes are parallel, the calculation can be made at 
once for both, the head to be stated being the sum of the two. 
With overhead feed, and wherever the return follows a different 
course, they are to be figured separately. The sum of the losses 
or the head required for the entire circuit can thus be established 
for some representative individual heat appliances in extreme 
location at lowest level and be compared with their actual heights 
above the boiler. 

If the available head is used up before the connections to these 
units are reached, or if the branches at the extreme end become 
larger than seems practicable, the mains will have to be en- 
larged, beginning at such parts which show the highest rate of 
resistance. Sometimes the conditions will make preferable a 
general increase of the available head by lowering the boiler, 
particularly where a large water contents is to be avoided. A 
system with short horizontal runs will often give opportunity 
for reduction of sizes, both for mains and connections. Some- 
times it will be found that individual branches to radiators at 
considerable elevation call for smaller sizes, theoretically, than 
seems desirable for durability and strength. In such instances 
it may be advisable to rely on adjustments by throttling, 
through key valves or other devices, but as a rule, it is best to 
reduce the size of the return branches for certain lengths, where 
least objectionable. Uneven sizes for flow and return, also 
reductions for odd lengths are indicated wherever the standard 
pipe sizes do not permit a reasonably close approximation of the 
available head. The losses of head for such portions of constant 
volume but uneven diameter are to be read off along the respec- 
tive velocity lines, with the extra resistance of the reducing 
pieces added as items of obstruction. If the sizes are changed 



HOT WATER HEATING BY GRAVITY 45 

by reducing elbows, the loss may be taken to equal that for a 
regular elbow of the smaller diameter. 

It is good practice in general to bring the resistance head to 
within about 10 per cent, of the effective head available, keeping 
the foi'mer lower than the latter as a factor of safety. It would 
be waste of time to carry the equalization closer, inasmuch as 
the limit of error in figuring, measuring, and through the uncer- 
tainties of execution, will make further approximation of ques- 
tionable value, and the discrepancies in the temperature of heat- 
ing surfaces are, in any case, much smaller than those of the 
resistance heads. The heat delivery, therefore, is kept within 
the probable errors in estimating the requirements, and fair 
distribution may be counted upon for any reasonable flow 
temperature, thus assuring the perfect means of central regula- 
tion. The calculation in itself will show why a true balance is 
never obtained by rules of thumb, and usually remains imperfect 
if based on approximation tables or effected by artificial adjust- 
ment. Unless a gravity system is balanced by calculation on the 
basis of head available and resistance offered, the discrepancies 
are liable to be very much greater. At best, the pipe sizes 
resulting from approximate methods are always larger on the 
whole than they need to be. They generally require higher 
flow temperature before the circulation is established throughout 
and involve greater bulk of water. Hence the scientific method 
will not only assure accurate heat delivery, but it will reduce the 
time for reheating materially and make hot water heating 
apparatus more responsive. 

The solution of these problems on a sound, physical basis will 
also show certain fallacies that have arisen through lack of un- 
derstanding. For instance, circulation does not depend on 
pitch, so long as the air can escape. Again, small pipes may be 
used without fear of clogging, if the means are provided to flush 
them. Nor will they rust on the inside. 

There is really no basis for the old notion that uneven sizes 
for flow and return should not be used. Delivery is governed 
by the resistance in the individual circuit as a whole, not by 
the smallest pipe size in any part of it. The variation in sizes 
for parts of the length of branches is a safe and practicable way 
of adjusting the resistances to the head available. The friction 
head in reduced connections can be foretold with greater cer- 
tainty than the effect of any throttling devices. It cannot be 



46 THE FLOW OF WATER 

disturbed or tampered with, and saves the vexatious process of 
adjustment during operation. 

The calculation as outlined may seem at first to require more 
time than is usually given up to such work when done by the 
popular approximation tables, but a repeated use of the charts 
will show the method to be practicable and more economical in 
the end. It is really based on the same principles as followed 
for years in doing accurate work by means of formulae and 
extensive tables. The charts, however, give a more convenient 
means of application and the procedure suggested should induce 
a clearer grasp of each problem as a whole. 

General Corrections. — As a rule, where higher temperatures are 
resorted to for the sake of economy it is also desired to use 
smaller piping. Aside from this, the assumption of smaller ranges 
for lower mean temperatures on the three charts is arbitrary. 
A pipe system computed by either of the charts will balance, 
practically, at any flow temperature, but the stated range will 
maintain only at the stated mean temperature. 

The ranges of temperature, however, on which these gravity 
charts are based will be found to give considerable differences 
in pipe sizes, and it is desirable, occasionally, to assume an 
intermediate range where extreme length of runs and other 
items of resistance, or the lack of height available would call for 
larger sizes of mains than seems practicable or economical and 
where one of the other charts would lead too far from the desired 
results. In" such cases a range of say 32° F. or 36° F. at the 
same mean temperature, will be indicated. The mean density 

W + Wi 

w + w. . . . . 2 

, remamms; the same, the effective height H varies 

2 ' ^ ' ^ Wi-w 

inversely as w^ — w, or the range of temperature. The volumes 
also are the inverse of the range. The B. t. u. on the charts are 
accordingly subject to correction by the factors giving the true 
volume, on the basis of which the resistances must be figured. 
The readings of the head are then to be corrected again for the 
corresponding differential head that is required to establish the 
balance. The calculation of a pipe system in other respects 
follows exactly the same course. It is not materially compli- 
cated, if the intermediate range of temperature is chosen to 
give a factor in even figures, say 10 per cent., plus or minus, 
so that it can be applied conveniently. 



HOT WATER HEATING BY GRAVITY 



47 



so'f: 




t-f% 



10" 20° 30° 40° 50 r. 

.Difference of Temperature between Ascending and Descending Columns 



Diagram B. — Table of differential heights for hot water heating. 



48 THE FLOW OF WATER 

The factors for correction are strictly applicable only to the 
stated mean temperatures, as the differential varies appreciably 
for cooler or hotter water, especially near to the boiling-point. 
The values given on the chart for 180° F. to 150° F. should only 
be used for mean temperatures near 165° F., and those on the 
other two charts for about 172° F. and 180° F. 

For other mean temperatures the factor for correcting the 
head will have to be established from the table of differential 
heights, which is an extract from the table of properties, made 
for the purpose of ready computation of the hydromotive force 
available for a liberal range of conditions. It gives the differen- 
tial density or pressure per foot of height, with the corresponding 
actual water columns, and the factors relative to the height of 
100.3 ft. on which the chart for 180° F. to 150° F. is based. The 
table is specially convenient for the solution of problems in 
which the variations of power with different mean temperatures 
should be considered. 

Using the table, we will find for instance, that the head for 
25° at 190° F. mean temperature is 110 ft. that is, it takes 110 ft. 
differential water column to produce 1 ft. of actual head. The 
factor for correction is therefore about 1.1. At 165° F. mean tem- 
perature and 25° F. range it would be 1 . 2. For 45° difference, at 
150° F. mean temperature, for another instance, the reading gives 
a factor of .73, while at 180° it would be .63. It is important 
to take into account these variations when dealing with higher 
temperatures generally, or with varying difference in one and 
the same system. At 220° mean temperature, for example, the 
same range of 30° results in a difference of weight of . 72 lb. per 
cubic foot as compared with .60 lb. at 165° F. thus reducing the 
head necessary to balance it from 100 to 83 ft. 

It is not often necessary to assume other mean tempera- 
tures for gravity systems, than those for which the charts apply, 
but it should be remembered in dealing with these odd cases, that 
the modified factors from the table apply, of course, only to the 
differential heads. The ratios on the chart for correcting the 
volume vary but slightly for other mean temperatures, and may 
be taken as constant in practice. 

Individual Corrections. — As stated previously, the balance of a 
gravity circulating system will depend on, or should result in, a 
uniform drop of temperature between all the rising and the falling 
columns, but a strictly uniform difference for all sets of branches, 



HOT WATER HEATINCx BY GRAVITY 49 

and for their entire height could only maintain if no heat losses 
occurred in transit. This condition is not often approached in 
practice to a degree that will make these losses altogether negli- 
gible. It is nearly always advisable, to take into consideration 
the heat emitted by the pipe system, and to neutralize its dis- 
turbing effect on the differential pressure by such increases of 
volume as will re-establish the assumed uniform drop for which 
the system must be balanced. Perfect balance involves an extra 
amount of water passing each branch corresponding to the heat 
losses and thereby securing even temperatures at return junctions, 
just as they are necessarily even at the junctions of the floio. The 
total tax in B. t. u., including the losses, should then equal 
W(t-ti) with both factors constant, that is with t-t^, and w^-w 
maintaining between ends, but decreasing for the height of columns 
in question. The total difference in weight, or the actual pressure 
which governs the flow, is therefore reduced to an extent depending 
naturally upon the levels at which the heat emission takes place. 
These variations from the assumed difference of tempera- 
ture can be calculated, and the actual difference in weight between 
the two opposing columns established from the mean density in 
each section. This gives the pressure available in pounds per 

W + Wj 

square foot or the head in feet of water of the density — - — . 

The differential height corresponding to the density w^-w, on 
which the calculations may be based, is found by simple divi- 
sion of that total weight or height by the differential density 
assumed. The result gives the mean height of the total heat 
emitted on the circuit which must balance the resistance head. 
The correct way of determining this mean effective height is 
the most accurate, but would require too much time in practice. 
A simpler method is to calculate directly from the heat loss and 
level of each sectional run, adding it to that of the appliance it- 
self. A loss of 20 per cent, along flow and return lines, for in- 
stance, at a mean level of, say, one-half the height h of the 
radiator above the boiler, would give an effective head of .2 X .5h 
= .lh. The radiator itself emitting the remaining 80 per cent, of 
head would produce .8h, making the true effective height avail- 
able .lh + .8h = .9h, on which the resistance should be based. 
Expressed in a different form we find again the mean level 

.2B.t.u. X.5h +.8B.t.u. X h 

H= — =.9h 

B.t.u. 



50 THE FLOW OF WATER 

which means that in the present case, the heat loss in transit, 
being below the point of delivery, will reduce its head by one- 
tenth. 

Since the heat units emitted by the appliance and by each 
section of flow and return piping is already marked in the schedule 
for the purpose of determining quantities, the most convenient 
way to estimate the mean effective height will be to multiply 
each item of heat loss in B.t.u. by the height above boiler at 
which it takes place, and divide the sum of the products by the 
sum of B.t.u. The examples to follow will further illustrate 
the method. 

It will be seen at once, that risers used as heating surface may 
have a decided effect on circulation, even when full allowance is 
made for the extra heat emission, unless they are sized for the 
corrected head. When balanced in this way, the difference 
t-ti will equalize itself at junctions, and the mean temperature 
will be even for each individual set of branches, but not neces- 
sarily for the heating appliance itself. With the greater part of 
the losses along the flow pipes, for instance, the radiator will 
be cooler, and vice versa with the losses greater on the return. 
Such deviations are appreciable only in odd cases, as occur for 
example with single main systems. They are properly corrected 
by increase or decrease of surface, making up for changes in effi- 
ciency in order to obtain the desired heat. 

Deviations of the true effective head from the actual height 

' of appliances, on the other hand, occur in nearly every apparatus, 

but are largely conditioned by the general scheme of distribution. 

The principal methods of piping should be considered mainly 

from this point of view. 

The Method of Piping. — Gravity circulation, as ordinarily under- 
stood, can be effected by underfeed, overhead, and by single 
main distribution with secondary circuits. The same principles 
as expressed in a general way naturally apply to any of these 
methods, subject only to the assumption of the proper factors as 
to height and temperature. These must be studied and clearly 
defined for each individual case before the final calculation is 
attempted. It is assumed, of course, that an apparatus be de- 
signed to exclude disturbance by lack of escape for the air, or by 
the generation of steam. 

Underfeed Distribution. — This method is distinguished by the 
location of both distributing and collecting pipes below the level 



HOT WATER HEATING BY GRAVITY 51 

of heating appliances. The mains and branches usually run paral- 
lel, either in the same or in opposite direction. The general idea 
is illustrated by Fig. 9. 

The heat losses along the mains, when insulated, are usually a 
small fraction of the total transmitted. While their bearing on 
the effective heights may become appreciable, it will affect all 
branches, more or less. The distribution is therefore not likely 
to be disturbed to any extent and no allowance need be made 
for the heat emitted by mains under ordinary conditions. For 
the branches, rising lines and individual connections, the losses 
are always relatively greater, and have more bearing on the head, 
especially when exposed, or only furred in, but not insulated. 
They should always be added to the tax in B. t. u. for flow and re- 
turn, as if a part of the radiation. If these losses occur on runs 
serving more than one appliance, as for instance on risers leading 
to several stories, they should be apportioned in round figures to 
the tax on individual connections, since any extra volume carried 
in these main risers will necessarily flow also through the branches 
beyond, distributing itself among the latter along the path of 
least resistance. If, on the other hand, parts of the mains are to 
serve as heating surface, their heat emission must be added as an 
extra tax, distributed as mentioned above for risers, and its 
bearing on the effective height should be established for all in- 
dividual circuits beyond. 

When sufficient heat is generated so as to keep the flow tem- 
perature slightly higher, to make up for losses along mains, and 
the radiating units actually emit the desired amount, the as- 
sumed drop of 30° F., 35° F., or 40° F., should then maintain very 
closely between- junctions, throughout the system. 

As a general rule for underfeed distribution, it will suffice to 
base the losses of head and by friction and obstruction simply 
on the heating tax in B. t. u. rounded up to include the probable 
heat losses in branches, risers and connections, but bearing in 
mind the slight reduction of effective height due to "the latter. 
The reductions of the effective height due to exposed rising lines 
and portions of mains, however, should be estimated from the 
heat emission and levels by one of the simpler methods, and 
taken into account. 

Example. — Fig. 11 represents the pipe schedule of an under- 
feed system for a residence, calculated for temperatures of 180° 
F. and 150° F. in flow and return. The horizontal runs of flow 



52 



THE FLOW OF WATER 



Open bends For 2" and larger 

All pipesincellarinsulafed. risers and connecHons 

bare and Furred in unless ofherwise marked 
R stands For exposed riser 
M ■stands For exposed horizontal pipe. 




Fig. 11. — Example of hot water heating with underfeed distribution 
180° F. to 150° F 



HOT WATER HEATING BY GRAVITY 53 

pipes were traced from the building plans and the vertical pipes 
are drawn to the same scale, under a fixed angle, so that all 
lengths appear in full and can readily be measured off. The 
levels of heating surfaces relative to the boiler are noted sepa- 
rately. The amount of surface to each radiator is stated, with the 
expected heat emission, depending upon style and height. The 
data in regard to insulation bearing on the heat losses in transit 
are also put on record. 

The thermal units to be carried by each section of the piping 
are added up from the individual radiating units down to the 
boiler, including the losses for all risers, approximately deter- 
mined and distributed among the individual connections. The 
preliminary sizes were then established on hand of the approxi- 
mation chart. The final sizes are obtained by the graphic method 
of calculating and balancing resistances, the example giving the 
result of the final revision, carried as far as the best practice 
will require. The figures in circles indicate the actual height 
in feet which will produce the differential weight necessary to 
overcome the total loss of head in flow and return system up to 
the respective junctions. The first number (1.6) for instance, 
includes the resistance of the boiler, with the connecting flow 
and return mains, up to the first branch. The second figure 
(2.05) includes the first, with the losses for the following 
section of the mains to the next set of junctions added to it. The 
factors for branch tees are always entered at the beginning of a 
sectional run, for the continuation of the main as well as for 
that branch, on the basis of their respective sizes. Proceeding 
thus to the individual radiators, where the circuit closes, the 
sum total for each point of delivery indicates the approximation 
between the available and required heads. If the actual height 
is greater, there is head to spare, and the delivery will be greater. 
It will be noted, that the figures for the first floor are all below, 
but close to the actual difference of level, which is 7 ft. For the 
second story they come well within the actual height, but the 
depression of the effective height through heat loss in risers, 
and the disadvantageous position under throttling, make a 
greater factor of safety advisable for radiators on upper floors. 

The example shows some instances where the risers figure as 
heating surface, giving the corrections therefore, as estimated 
from the heat emission at different levels above the boiler. In 
the case of a coil in a flow riser the depression of the mean ef- 



54 



THE FLOW OF WATER 



fective height due to the chilling of that line on a lower level, 
is seen to be a considerable item. It would ''spoil the draught/' 
so to speak, for the radiator on that riser, unless the pipe sizes 
are based on this reduced effective height. 

Overhead Distribution. — The distinguishing feature of the 
overhead system is a main flow pipe rising from the boiler 
to the highest point of the apparatus, with the distributing 
lines starting at that level and feeding the radiators from above. 
The returns are located below the leyel of radiation. A typical 
arrangement is illustrated by Fig. 12, 







hm -- mean effect i ve height for f-f, 

e -heaf losses in B.tu. per hour for sections 

E = total heat carried on individual circuits 

Fig, 12. — Schedule of hot water heating system with overhead main. 

The main riser in this case represents the lighter ascending 
column, while the rest of the system, made up of the distributing 
and collecting mains, branches and risers, represents the heavier 
descending columns. The latter are naturally of the same total 
height, but in sections of varying density, the upper ones being 
made up of the feed lines to radiators, which are always a little 
cooler than the main rising directly from the boiler, and would 
create a circulation by themselves. With this arrangement the 
heat losses are, as a rule, relatively small in the main riser and 
greater in the branching feed lines overhead, thus placing the 
heat emission in transit at a higher level as compared with the 
underfeed, and thereby creating an increase of effective head or 
additional pressure. Whether this greater motive force is 
sufficient to overcome the extra resistance presented by the 



HOT WATER HEATING BY GRAVITY 55 

main riser, will appear from the calculation of a system, with 
proper application of all factors. Unless structural or other 
reasons are decisive, this calculation should determine the method 
of piping to be used. Where radiators must be placed near to 
or even below the boiler level, the overhead system may give the 
opportunity to create sufficient extra head to assure circulation. 
In such cases it is often the only practicable solution. 

Under ordinary conditions the heat losses in transit should be 
taken into account to the same extent as for an underfeed system. 
That is, they may be neglected for insulated mains, at least as 
far as they will affect all branches alike. Inasmuch as the 
differential weight is increased in this case, the branches further 
away are under no disadvantage. The heat losses on the indi- 
vidual branches and vertical feed and return lines from the attic 
to the cellar should always be added to the tax on the system 
in B. t. u. considering them as portions of the heating surface. 
The extra volume provided thereby will then practically make up 
the volume of water necessary to maintain the desired tempera- 
ture difference between the flow and return mains. 

If the overhead system is used with the idea of securing the 
increased mean effective head, the main riser should always be 
insulated, since any heat loss on the same will depress the mean 
level of cooling surfaces and reduce the head available for circu- 
lation. When the overhead feed is installed for different reasons, 
the heat loss can be made up by higher initial temperature, and 
does not bear on the distribution, as long as allowance is made 
for it. In either event, nearly all the heat emission with this 
method of piping occurs in the descending line. For appliances 
at low level, and at long distance from the heater the losses take 
place in greater part above the heating surfaces proper, and have 
relatively more bearing on account of higher mean temperatures 
involved. The risers for radiators at high level, near the main 
riser, on the contrary, show most of the losses below. The 
bearing of these facts on the head available should be established, 
not only for the proper balance of the system, but also for utilizing 
the opportunities peculiar to overhead feed, of creating extra 
head where most needed. 

The method of doing this has already been outlined, and is 
further explained, as applied to a variety of conditions, in Fig. 
12. With a single radiator on the circuit returning directly to 
the boiler, the problem is simply one of finding the sum of differ- 



56 THE FLOW OF WATER 

ential weights for the several parts of the circuit (w^ — w)hJL + 
(w2— w)h2— (W4— W3)h3 and dividing the sum by the difference 
in density for the full temperature range (w^ — w) intended. 
This will give the mean effective height h^^^ for which the 
resistances are to be balanced. It is the accurate way of calcu- 
lating the pressure available, as it takes into account the greater 
variation in densities at higher mean temperatures. For practi- 
cal purposes, the process is too slow. The quicker and more 
convenient way is to figure again the mean level of cooling 
surfaces, from the heat emission of the individual runs e^ q^ q.^, 
which are already given, and their height above the boiler, 
h^ hg hg, which can be measured. With two or more units on 
the same set of risers as shown next, the heat emission on the 
common runs should be apportioned to the volumes passing the 
individual branches. In practice it will suffice to do this in 
round numbers, or to consider it simply in rounding up the 
figures for each branch. 

The calculation of the effective head becomes of vital impor- 
tance when parts or all of the appliance proper is located below 
the level of the heater, and the balance of the circuit must provide 
the head necessary for circulation. The same will apply when 
radiation is inserted in sequence, instead of in series. In such 
cases the mean temperatures for each unit should be estimated 
and allowance made for varying efficiency. This is also advisable 
with long exposed flow connections. 

Example. — In the example shown by Fig. 13 the corrections 
to the effective height average about 2.5 ft., while for the 
underfeed it would probably be about — .5 ft. The extra 
length of the main riser uses less than 2 ft. additional head. 
The gain might reduce the size of a few connections, but would 
not permit a reduction in the size of the mains. Overhead 
distribution in this instance justifies itself rather on account of 
the fact that heat emitted by the overhead piping serves a 
useful purpose, and incidentally permits the entire system to 
vent itself through the expansion tank, which is a desirable 
feature in many cases. 

For one of the circuits the temperatures and densities are 
figured accurately from the amount of water circulated and the 
stated heat losses along the line, giving the actual difference in 
weight and the water column for 40° F. range. The effective 
height for the branch is appreciably higher than that which 



HOT WATER HEATING BY GRAVITY 



57 




^ ^ ^ 
(T3 ro ^ '^ 



f- 



f^ 



■+- 



c: c: "5 c: 

o S ii ^ 

'C '^ '- w 

1: ^ ^ ^ 



f— 



^-. 



J- o-,oz — V 

J 



2^1 



„0-,8Z 



4 



S,9 



o->H 



bB o 

fl o 
•43 "O 

-S3 



■-*J,o-e- 



58 



THE FLOW OF WATER 



was found by the easier method, but the difference is too slight 
to affect the pipe sizes in this case. For the other circuits the 
mean effective heights were figured in the usual way, as the 



ratio of 



eh + eihi+ etc. 
E 



, each item of loss being stated, together 



with the estimated mean level at which it takes place. The 
results are underscored and marked together with the sum E 
for each branch, at the respective junctions. The system is 
balanced for 40° F. difference, at 180° mean temperature. It 
will be seen, that the resistance heads (in circles) figured from 
the chart, are always kept a fraction below the mean effective 
head. 

It may be noted in studying this example, that overhead 
distribution gives good opportunities for accurate balance by 
omitting or providing insulation for certain runs above or below 
the appliance with the idea of increasing or reducing the effective 
head for certain branches. Such expedients are not proper, of 
course, where heat is wasted thereby or becomes objectionable. 

Single Main Distribution. — Fig. 14 is a schedule showing the 
method of piping generally known as the '^one-pipe system," 




Fig. 14. — Schedule of hot water heating system with single distributing main. 



but more correctly termed '^single main system with secondary 
circulation.'' This single main, forming a complete loop between 
the outlet and the inlet of the boiler, may be considered as a 
distributing drum while the branches to the individual heat 
appliances are all separate, independent circuits starting from 
and returning to this drum. 

When the temperature is kept up along the loop some circu- 
lation is almost bound to occur in each of the individual circuits. 
Distribution of the heat by this arrangement does not depend 



HOT WATER HEATING BY GRAVITY 59 

as much on distances of radiators from the boiler, as it does on 
their elevation above the main and the general decrease in 
temperature along the same. The individual circuits are inde- 
pendent and do not have to be balanced among themselves. 
Fair results can be assured with this method of distribution by 
the old, wasteful rule of ''making sure" by having the pipes 
large enough all around, which, by the way, will often fail with 
the two-pipe idea. Accurate calculation is nevertheless desirable 
for reasonably close distribution, to reduce the bulk of water, and 
for economy. 

The first condition to determine is the drop of tempera- 
ture along the main, under which it will circulate, and which 
should be kept small if it is desirable to maintain a high effi- 
ciency of heating surface throughout. For a greater drop the 
difference t^-t', or tg-f' between the risers to and from appliances, 
should be larger at the warmer end, and smaller at the cooler end 
of the main line. Smaller differences result in higher mean tem- 
peratures, which will make up, to an extent, for the decreasing 
flow temperatures in the secondary circuits. The differential 
weight w^-w thus changes for each set of risers and likewise 
the available pressure (Wi-w)hj. The several sets should be 
figured independently for that reason, the problem being to 
find the size of pipe which will give about the right value for 
t^-t', or that which would assure the expected efficiency of 
heating surface. Such graduation is not always necessary, 
where the loop serves a single room, or in" other cases where 
the decreasing efficiency happens to be immaterial. If the 
main is looped vertically, as shown to the left on Fig. 14, the 
heights hj, h.^, etc., can be figured out for a desired drop in 
temperature and the connections lengthened to make up these 
heights. 

The effective height h governing the flow in the primary circuit 
is the difference between the mean level of the boiler and that of 
the several tappings where the cooled water rejoins the main. 
Since the difference in temperature should be small, the available 
height will generally determine whether the method is practicable 
or economical in a given case. A vertical loop usually permits 
a smaller drop to be maintained, and effects closer distribution, 
at less accurate balance. A horizontal loop is only advanta- 
geous when it can be placed at a good elevation above the boiler. 
It generally requires, the grading of individual branches 



60 THE FLOW OF WATER 

to make up for the decreasing temperature along the main. 
When well insulated, as it should be, the main is likely to emit 
only a small fraction of the total heat carried, but it will pay to 
take the losses into account, because, with a horizontal loop, they 
will increase the differential density for nearly the entire height 
available, and with a vertical loop usually for a considerable 
elevation. The heat losses for the risers and connections of the 
secondary circuits, especially when used as heating surface, 
should be included again in the tax, and allowance made for the 
reduction of the mean effective height in the same way as would 
be indicated for an underfeed or overhead system. 

Example. — In the example presented by Fig. 15 the loop was 
first calculated for a difference of 20° F. between the two ends of 
the main, but the head required for a reasonable pipe diameter 
was found to be larger than the head room permitted. Since the 
elevation of the main above the boiler could not be increased 
beyond 8 ft. without prohibitive expense, the differential tem- 
perature at which the resistances would balance that height was 
found by tentative process to be 25° F. for a 6 in. main carrying 
nearly the total volume for the entire length. This range made 
it desirable to graduate the individual circuits, so as to keep the 
mean temperature of radiation within narrower limits. The 
resistances, accordingly, were decreased for the successive 
branches, starting at the flow end, so that the differential weight 
required, and the resulting temperature, would correspond about 
with the efficiency of surface as it decreases along the main 
circuit. This had to be done again by tentative calculation, 
using the factors for general corrections as to range, for a mean 
temperature averaging about 165° F. As will be noted, the drop 
for the successive branches decreases with the flow temperature 
toward the return end of the main, the lowest efficiency of the 
heating surface being thus kept up within about 85 per cent, in- 
stead of dropping to less than 70 per cent, without graduation. 
In the latter case, if no difference were made in sizes, the range 
would naturally increase toward the return end owing to the 
smaller differential weight at lower mean temperature, which 
must be made up by a greater drop. In this particular instance 
the drop would have increased about from 28 1/2° F. to 32° F. for 
mean temperatures ranging from 178° F. down to 153° F., as shown 
by the lines of equal height on the table of differentials. 

To secure a fair graduation of the drop it has been necessary 



HOT WATER HEATING BY GRAVITY 



61 



•51-13500-@ 



51-15100 -(fD) 



•48-7800-@ 




)/.^ /' .§^##/ /^ § ##/ / .? #J/,5700/ 16? 

5400 ^VS),. .Jf, 



Fig. 15. — Example of hot water heating with single distributing main. 

Levels and Difference of Temperature. 

Main pipe in cellar 8 ft. above mean level of boiler. 

Drop in temperature between flow and return ends of main 25° F. Mean 
temperature 180° F. 

From mean level of main to radiators on lower floor 4 ft. 

From mean level of main to radiators on main floor 15 ft. (Effective 
height about 14.5 ft.) 

From mean level of main to coils at gallery 23 ft. (Effective height 
about 21.5 ft.) 

Drop in temperature for individual connections 40° F. to 20° F. Mean 
temperature 158° F. to 174° F. 

Main pipe and branches insulated up to main floor. 



62 THE FLOW OF WATER 

in this case to use flow and return pipe of uneven sizes for some 
of the circuits. The necessity for this will occur more frequently 
with this method, if calculated as it should be, since the resistance 
head is made up by a single set of branches, usually very short, 
and cannot be varied by changes in parts of the main. The con- 
nections with the main, however, may be changed sometimes in 
length, with a view to modifying the resistances. This has been 
done in the example shown, where the length of runs between 
main and vertical lines is graduated in a general way, giving 
greater resistance where extra pressure is available. This ex- 
pedient will also frequently help to balance an underfeed or over- 
head system. Local conditions, of course, must always deter- 
mine or suggest the most practical ways and means. 



THE FLOW OF STEAM 

CHAPTER V 

THEORY OF THE FLOW 

Properties of Steam. — The relations of pressure, volume and 
temperature of steam are presented graphically by an adaptation 
of Dr. R. Mollier's^ Entropy diagrams, based on Callendar's 
formula. The results from the latter deviate slightly from older 
data in certain respects, but seem to be borne out by more 
recent research. No attempt has been made to incorporate all 
the refinements needed for design of turbines and other steam 
motors. Although the diagram is made up in compact form, 
for the sake of better illustration, the readings of pressure, 
volume, temperature and density should be accurate enough for 
purposes of heating engineers. Separate scales are given for 
absolute pressures and temperatures. The latent heat can be 
deduced by subtraction from the total of the sensible heat, 
which is given by the temperature. The arrangement permits to 
follow the variations of the quality of the steam due to increase or 
decrease in the amount of heat, incidental to long distance trans- 
mission. It gives also the changes in pressure and volume, or 
work performed. The variation between the initial and final 
state can be traced by a line on the diagram, which will either 
approach the curves of equal heat or the lines of equal pressure. 
Rapid pressure drop for instance, due to high resistance, indi- 
cates the work performed and reconverted into heat, the line 
keeping more closely to those of equal heat. The extreme of 
pressure drop without heat losses is reached by the adiabatic 
expansion of steam, or the discharge through a frictionless nozzle, 
in which case the expansive force will bear on the volume de- 
livered. In ordinary heating practice the changes follow more 
closely the isothermal lines, the variations of pressure being gen- 
erally a small fraction of the total, absolute, under which the 
steam is transmitted. The analysis on hand of the table is useful in 
showing whether the changes in pressure and density as affecting 

^ Dr. R. Mollier's neue Tabellen und Diagramme fiir Wasserdampf. 
Springer 1906. 

63 



64 



THE FLOW OF STEAM 






-^60 



Pressure of Superheated Steam 
5\ let 7/ 8i 91 Wl I I ZO \ 30 




2 .1 .09.08 .07 M .05 .04 .05 

Density, or Weight oF Steam per cu. Ft 



Diagram C. — Properties of steam. (Adapted from Dr. R. Mollier's Diagrams (1906), 
based on Callendar's formula.) 



THEORY OF THE FLOW 65 

the volume and velocity are negligible in a given case. It will 

show also whether a certain pressure drop by resistance of a 

conduit, accompanied by a certain heat loss, will result at the end 

of the line in w^et, saturated, or superheated steam. The lines 

will give the amount of condensation per pound of steam, or the 

degree of superheat, as the case may be. The variations in 

volume, due to condensation are also appreciable, and often 

bear decidedly on the resistance by friction and obstruction. 

Friction in Pipes. — The velocity for calculating the resistances 

to the flow is naturally based on the volume passing a given run 

W per hour 

of conduit. It IS expressed by v = and must equal 

3600 wa 

I — ¥ . . . 

\1 2g — ^ w^herein P^^P— (Pf +Pj.), or the velocity head resulting 
^ w 

under the friction and other resistances. W is the weight per 

hour, w should be understood to be the mean density main- 

W 

taining along the run, and — the mean volume. Since the 

w 

density varies considerably for the range of pressure that may 

come in question, the quantities are better stated in units of 

weight, as the absolute measure. 

High pressure steam for power purposes is usually measured 
in pounds per hour, or in h. p. based on the standard of 34.5 lb. 
of water evaporated from 212° F., or of 30 lb. from 100° F., into 
steam at 70 lb. pressure per square inch. As a heat carrier, it 
can be assumed to transmit roughly 1000 B. t. u. per pound, 
since the total energy given up when utilized for heating is 
nearly always more than the latent heat at 70 lb. The high- 
pressure chart is accordingly based on weight and approximate 
heating capacity, the horse power being derived by simple 
division w^ith the equivalent 33,000 B. t. u. 

Low-pressure steam for heating can be rated closely by the 
thermal units it will yield in condensation. If the pressure in 
appliances varies but slightly from that in conduits, the heat 
carried will not exceed materially that of evaporation. The 
quantities in B. t. u. from which the lines are computed there- 
fore correspond to the latent heat per pound. 

Among the formulse giving the loss of pressure by friction in 
pipes, that of D'Arcy is often applied to the flow of steam. Ex- 
pressed by the height of a column of steam it makes the friction 



66 THE FLOW OF STEAM 

head hf = C -— , wherein C is a coefficient varying with the diam- 
eter of the conduit. 

Another generally accepted expression is one credited to Bab- 



wpfd^ 
cock for the weight of steam W = C — or for pressure 



4( 



-¥ 



loss Pf ■== -. In this formula C is a constant. Bab- 

C^wd^ 

cock states it to be 87. Carpenter finds it to be 87.45. 

Die "Hlitte'' quotes the formula derived from the experi- 

1W2 
ments by Gutermuth, making the friction loss Pf = C — -- which 

wd^ 

corresponds to D'Arcy's form for hf, except that no variation of 

C is given. 

As applied to high-pressure steam flowing through insulated 
piping under comparatively small drop, and with W as the initial 
weight; these formulae have been found to agree substantially in 
practice. For low-pressure steam, where the loss of weight in 
transit is a greater item, as a rule, the results from formulae by 
German authorities on heating, differ materially from the above. 
In so far as they cover the effect of condensation, the latter are 
likely to come nearer to the facts. The well known expressions 
by Rietschel, Fischer and others agree closely among themselves 
and may be accepted as the most accurate for the range of diam- 
eter and velocities met in heating work. • 

Fischer's expression of which all others are modifications, 

al /W + 0.5WA2 ^ .,,,., 
gives the pressure loss Pf = ^ ( ^ I , wherem W is the 

weight of steam delivered, Wj the weight of condensation 

dropped in transit, p^^ the mean absolute pressure, and a is a 

constant applying to any diameter and velocity. 

Taking the general formula used by Weisbach for expressing 

1 v2 . . . W 

friction loss Pf = w.f -- — and substituting for v its value 

^^ d 2g ^ 3600 wa 

1 W242 1 W2 . 

we obtain Pf = w.f- ^^^^, , ,, ,^ =Cf -- — m which form C is 
d36002wM%22g d^ w 

a constant, and f is presumably variable, as for water and for 



THEORY OF THE FLOW 67 

air. Comparing the results from these formulae with those for 
water, it appears that the influence of diameter and velocity on 
the coefficient f is less pronounced with steam, or that the friction 
head varies more nearly as the square of the velocity, and 
inversely as the diameter. To find the approximate variation, 
the friction heads figured according to the above authorities 
were charted on logarithmic paper, and the average slope estab- 
lished for the lines of velocity and diameter. The angle of these 
lines gives the exponents for the hydraulic radius and slope in 

vy 
Tutton's general expression v = CR^S^ or Pf =w.f ~^1. 

d^ 

In this formula, v is the mean velocity as it may result under 

condensation and pressure drop for the length 1, that is, v 

should correspond to the volume of steam passing a certain point 

somewhere between the two ends, representing the center of heat 

and pressure losses. 

The average of lines for high-pressure were found by this 

graphic presentation to take on a distinctly different slope for 

those of low pressure, as derived from the German authorities, 

if based on an equal volume. The variation of the slope, or of 

the exponents for v and d would therefore seem to indicate the 

bearing of the density and temperature on the viscosity. This 

is confirmed again by the investigations of Biel previously 

referred to, which cover various kinds of fluids and conduits. 

The value for f, derived from the charted pressure losses, with 

the exponents established, was found to be nearly equal to that 

for water. Inasmuch as the same kind of piping is generally 

used, the identical value has been assumed. Inserting these 

figures in the basic formula, the pressure loss by friction is for 

y 1.95 

high-pressure Pf =w .0257 - ^^ 

V 1-97 
for low-pressure Pf = w . 0257 —r^^ 

The exponents given here apply only to saturated steam at 
or near 70 lb. per square inch and for low pressure steam slightly 
above atmospheric pressure as used for heating. Superheating 
bears distinctly on the friction head, but these variations have 
not yet been fully established. Since the friction seems to 
decrease with the degree of superheat, it will be safe for most 



68 THE FLOW OF STEAM 

purposes to assume the loss of head equal to that for saturated 
steam at the same pressure. The charts must necessarily rep- 
resent average conditions. Inasmuch as they agree in general 
with the results from the standard formulae quoted, they should 
give conservative values, at least for all conditions occurring in 
heating practice. 

Local Resistances. — The general formula for the loss of 
pressure through various forms of obstruction as applied to the 
flow of steam, will show the exponents for v conforming to 
those given for the friction head. Thus we find, 

^1.95 

for hi&h-pressure Pr. = w 1 . 12r 

^ ^ ' 2g 

yl.97 

for low-pressure Pr = w 1.07r — — 

v2 
The factor r corresponds again to the velocity head — at 10 ft., 

102 ^ 102 

hence the constants are — =1.12 and =1.07, respec- 

jLQi-95 10^-^^ 

tively. The values of Pj. for steam will decrease very little with 

higher velocities, so that for speeds above 10 ft. per second, they 

v^ . - 

will be but slightly less than r — . This shortage, however, is 

justified again, since the true coefficients for the high velocities 
in question are probably smaller than those generally quoted, 
which have been derived mostly from experiments at lower 
velocities, with water. The factors r for the various forms are 
identical to those for water in so far as the same style of pipe- 
work and fittings are used. The composite given for radiators 
includes the resistance of one angle valve only and an allowance 
for obstruction within, which is applicable to header coils as 
well. The return bend type should be calculated as runs of 
piping, at decreasing velocity, taken to be one-half the initial, 
assuming that no steam escapes at the return end. The factor 
for boilers includes the obstruction presented by outlets with 
nipples, header or dry pipe, in either of which the velocity head 
is lost and recreated repeatedly. 

Probably because in common practice the pressure in steam 
heating systems is kept much higher than needed to effect distri- 
bution, the resistances to the flow have so far not received due 
attention. As shown later, it will pay to ease the flow of steam. 



THEORY OF THE FLOW 69 

at least with certain methods of piping. Those types of fittings 

intended to reduce resistance are for that reason included in the 

list. 

Velocity Head. — The losses of momentum as they occur in 

high pressure steam piping and heating apparatus are practically 

all incidental to the forms of obstruction as tabulated, the factors 

for which include them. Only a sudden decrease of velocity 

due to other features is to be taken into account. The loss of 

motion incidental to the drop in dynamic head is to be estimated 

v2 
and entered as a fraction of Pv = w — , the values of which m 

^2g 

pounds per square foot or square inch are readily found by the 
special line for the velocity head on all the charts. Gradual 
changes in speed, through tapers, seldom occur in heating work. 
The resistance of such special pieces may be estimated generally 
on the same principles as outlined for water and air, except in 
cases where expansion is liable to take place and affect the result. 

The dynamic head at junctions and the relations to the 
static head often bear on distribution and are to be considered 
from similar points of view as explained relative to water. 
Occasionally the momentum is to be considered also when 
moist steam is carried and it is desired to separate the water. 

Energy Expended in Flow. — Analogous to the work expended 
in pumping water, a certain energy is used in conveying steam 
through a system of piping, as expressed by the drop in potential 
caused by the movement. This energy, being reconverted into 
heat, offsets to a greater or less extent the losses by convection 
and radiation in transit. It affects the total thermal loss only 
in so far as the steam temperature is influenced thereby, and 
through the use of smaller pipe sizes resulting under greater drop 
of pressure. These thermal changes should be established 
wherever it is desirable to know the quality of the steam delivered, 
that is, its state of dryness as affecting the efficiency of motors, 
or when advantage is to be taken of the heat developed by fric- 
tion and other resistances with the idea of assuring delivery of 
dry steam, or for economy in installation. The diagram of 
properties will be helpful in such investigations. 

Expressed in B.t.u. per hour, the reconverted energy is 

2545 AV 144 (Pf+PJ W 

;^ ^ =.185 — (Pf+PJ. The equivalent for the, 

w 3600.550 w ^ ^ ^ 

work represented by the motion itself, or the velocity of dis- 



70 THE FLOW OF STEAM 

W 

charge which is . 185 — p„, can be coDsidered as heat delivered. In 
w 

practice p^ is usually a small part of the total pressure loss, and 

. . W 

it IS safe to assume the energy to be simply .185 — P, or .185 Q.P. 

w 

Subtracting it from the heat losses in transit by convection and 

radiation, we find the net thermal loss in transmission, and from 

it the heat delivered. The relation of these two factors in reality 

determines the delivery and it would seem correct in principle 

to calculate a system of conduits directly on the basis of the 

thermal changes by the means of entropy diagrams arranged for 

the purpose. In heating practice, however, the energy expended 

in the flow is relatively small, and the drop in pressure alone will 

practically govern the discharge, hence it is made the basis for 

computation in the same way as for the flow of water and air. 



50 60 70 ao 90 



CHART V 

HIGH.PRESSURE STEAM 

At 70 lb. per sq.ln. Mean Pressure 

THROUGH STANDARD WEIGHT IRON PIPES 



W per hour 



3600Xii'Xa 1000x3600xirxa' 
i.in. to overcome friction 7'/ =777 0207— — tth- 



Enei^ of flow in B.t.u. per Y 
The weight of 8t«ara or 1 



5irp.h.l44(Pi-P, 



X550 

should i 



. transit on and beyond t 
take roughly for 

outdoors, per sq.ft. s 

doors, per sq.ft. surface, 
itdoora, per sq.ft. surface, 



idc the loss \ 



q.ft. surface, 1(K) B.t.u. =.10 



When the volume decreases appreciably by condensatio 



art and any obstructions 
For other mean pressui 



1.76 for 30 
1.47 for 40 
1.27 for 50 



each with the r 



It 13 necessary to figure straight 
d of the initial. Irregular runs 
2 of flow through the respective 

iction, resistance and fiow, for 



.91 for SO ■■ ■■ 


59 for 140 




55 tor 150 


.77 tor 100 " •■ 








.67 for 120 " " 


40 for 200 




p-h. fnc/ud/'na Loss in Tra 



CHAPTER VI 
HIGH-PRESSURE STEAM DISTRIBUTION 

Chart V. — The chart for calculating high-pressure steam pip- 
ing is intended mainly for transmission of heat by live steam at 
long distances, where the pressure losses materially influence 
delivery. It is also convenient for the proportioning of pipes 
for power purposes. 

The quantities are given in pounds of steam per hour, from 
which the B.t.u. carried for heating purposes can be figured by 
simple multiplication, 1 lb. corresponding practically to 1000 
B. t. u. The pressure losses are expressed on this chart for a pipe 
length of 10 ft. in the customary measure of pounds per square 
inch, as against pounds per square foot used for the low pressure 
diagrams. 

The auxiliary diagram facilitates the approximate sizing 
of a line or system for different pressure to be carried, for a rate 
of loss of 1 lb. per 100 lin. ft. The line for sizes of returns will 
apply practically to either of these, except in cases where un- 
usual resistance is to be expected, or when returns must carry 
a considerable amount of steam. 

Data is added for estimating the heat losses in transit, which 
should always be looked into, and the quantities corrected 
accordingly. Factors are also given for correcting the losses by 
friction and local resistances for a liberal range of mean pressures, 
the charted values being accurate only for 70 lb. gauge. 

Outline of the Problem. — The sizes of steam pipes should be 
determined by the drop of pressure permissible in transmission 
rather than by the absolute mean pressure carried. This prin- 
ciple applies to all classes of work. All problems in distribution 
and discharge should be considered from this point of view. 

For power purposes, when the potential energy is to be utilized, 
the leading idea should be to reduce the resistances to the smallest 
practicable fraction of the initial pressure. When delivering 
steam to reciprocating engines, or other apparatus with inter- 
mittent flow, the pressure loss is difficult to compute. It will, 
in any event, seldom pay to attempt an accurate calculation since 

71 



72 THE FLOW OF STEAM 

the piping should be ample to act as an intermediate or supple- 
mentary steam reserve. Sometimes its weight and strength in 
resisting vibration are governing factors. But in any case it is 
desirable, as stated, to ease resistances and reduce the loss of 
potential as far as practicable. The chart for approximation 
gives fair average sizes for power work at various pressures, 
which may be rounded up or reduced according to length of runs 
and other conditions. Only for the transmission of power to dis- 
tant points it is advisable to calculate the loss of pressure by 
means of the other chart in order to establish the initial pressure 
required, or to verify the final pressure available, as the case 
may be. No general rule of approximation can be given for 
such work. Each case should be considered on its individual 
merits. 

For heating, the problem is essentially different. High-pres- 
sure is used either for the sake of high temperature, as for in- 
stance in drying coils, steam tables, cooking and a variety of 
technical purposes, or it may be used simply for the economical 
transmission of steam or heat at long distance. In either event 
the pressure loss, not the working pressure, is the factor governing 
the pipe sizes. 

When steam is distributed to miscellaneous appliances, in use 
at odd periods, it w^ill not pay to equalize the pressure drop 
in the pipe system for the quantities to be delivered at various 
points, but a rough calculation should be made of the total loss 
to the apparatus furthest from the source, or that requiring the 
highest final pressure. This will naturally lead to the sizing of 
the main line on the basis of the heaviest tax, and provide thereby 
a certain reserve capacity, which is always desirable under 
fluctuating load, if only on account of the extra flow for reheating. 
For the approximate sizing of such a pipe system the diagram 
giving the lines of 1 lb. per square inch friction loss per 100 lin. 
ft. will again be found convenient. The total drop of pressure 
is then to be computed by means of the other chart, with due 
allowances for mean pressure above or below 70 lb. per square 
inch. 

Where high initial pressure is wanted for the economical 
transmisson of heat for long distances, the pressure drop may be 
a considerable fraction of the total, and equalization between 
several points of discharge is desirable, even though reducing 
valves are to be used. Theoretically, reducing valves are not 



HIGH-PRESSURE STEAM DISTRIBUTION 73 

necessary, if the excess pressure is used up in transmission. To 
make the resistances of the line equal to this excess between the 
initial pressure and that desired at heating surfaces would be the 
ideal or scientific method wherever steam is delivered only at one 
point, or where the final pressure at several points is to be equal, 
and fluctuations in delivery take place at the same time. Whether 
the ideal method is practicable depends upon the conditions 
presented in individual cases. A long main line, for example, 
without branches up to a certain point, is advantageously sized 
to give such a pressure drop that will keep the steam dry, or 
will even superheat it by the friction, and to sacrifice, up to that 
point, the greater part of the available head. The further lengths 
of main and branches may then be equalized with sufficient 
accuracy by intelligent sizing, occasionally requiring a reduction 
for portions of individual runs. Branch pipes may figure very 
small when sized on this principle. There are, of course, practical 
limits to the velocities, particularly as to noise, although the 
probabilities in this respect are less than they will be if the steam 
is throttled at one point by a reducing valve which would pre- 
sent smaller area than a pipe reduced in size for a considerable 
length. 

Distribution under Varying Pressure. — The condensation of 
steam in heating apparatus generally fluctuates within wide ranges, 
and the total pressure drop is about proportional to the square of 
the volume delivered. It seems essential, therefore, to investi- 
gate the bearing on distribution of variations in the delivery, 
which is controlled by the condensing capacity of the apparatus 
or appliance, if no steam escapes beyond. For reheating, the 
amount of steam is limited as a rule by the supply available, but 
it may easily be 50 per cent, in excess of the flow under normal 
conditions. When a building is overheated, condensation may 
be reduced often as much as one-fourth, even with all 
radiation in use. These variations are liable to be simultaneous 
for a whole system. Taking for example two branches, one to 
carry normally 1000 lb. of steam for a distance of 300 ft., the other 
4000 lb. for 150 ft., each with a drop of 4 lb. at, say, 70 lb. mean 
pressure. On the chart for friction head per 10 lin. ft. the nearest 
size for the former branch is found for a rate of loss equal to 

4X10 

- = . 133 lb. per sq. in., which, for 1000 lb., is closely 

met by a 2 in. pipe. The 4000 lb. must pass through the other 



74 THE FLOW OF STEAM 

4X 10 
branch at a rate of — - — = . 267 lb. and require a 3 in. pipe. 

The pressure losses figure 4. 05 lb. and 3 . 9 lb. respectively. For 
a flow increased by 50 per cent., or 1500 lb. and 60001b. of steam, 
the corresponding losses are found to be 9 lb. and 8.7 lb,, and 
for the decreased tax of 750 lb. and 3000 lb. we find the losses 
to be 2 . 30 lb. and 2 . 25 lb. The equalization under varying load, 
therefore, is affected only to a very slight extent, that is, only in 
so far as the velocity and diameter bear on the coefficient of 
friction. A reasonable number of local resistances would make 
little difference on this result. Since the resistances for steam, 
when compared with water vary more nearly with the square of 
velocity, the equalization may be said to maintain under the 
common fluctuations of load, such as are caused by the daily 
reheating and by weather conditions, when affecting all branches 
alike. 

Distribution under Throttling. — The effect on the flow in one 
branch through the throttling of others depends largely upon the 
increase of condensation under greater pressure or higher tempera- 
ture. Such increases of temperature within heating appliances 
as are likely to result through variations of the pressure loss in 
transit are appreciable in a distributing system designed for an 
excessive pressure drop. Taking the same example of 300 ft. of 

2 in. pipe and 150 ft. of 3 in. pipe for illustration, and assuming 
they are supplied by a 3 1/2 in. main 600 ft. long, we find the 
pressure loss up to the junction to be about 12 lb. per square 
inch for the normal amount of 5000 lb. carried. With the 3 in. 
branch shut off, the 3 1/2 in. main will supply only the 2 in. 
branch, normally discharging 1000 lb. Leaving out of con- 
sideration the greater loss of heat in transit up to the junction, 
we find the drop of pressure in the main will be only about . 57 
lb. for 1050 lb. instead of 11.8 lb. for 5000 lb. through 600 ft. of 

3 1/2 in. pipe, while that for the 300 ft. of 2 in. pipe is increased 
to 4.5 lb. for 1050 lb. The -steam is thus delivered at a drop 
of 5.07 lb. instead of 15.8 lb., or at a final pressure nearly 
11 lb. greater, with correspondingly higher temperature, in this 
case about 9° F., which would approximately increase the con- 
densation to the extent assumed. Even in such an extreme 
case the delivery is therefore affected only by a small percentage 
and, ordinarily, throttling may be said to have little bearing on 
delivery in a closed system and with equal chances for steam to 



HIGH-PRESSURE STEAM DISTRIBUTION 75 

condense. Conditions will differ, of course, when the steam is 
discharged through reducing valves, or delivered against at- 
mospheric pressure. In the latter case the relative increase in 
the final pressure would control the discharge. 

Periods of throttling or shutting of branches are naturally 
followed by periods of reheating, during which the flow to the 
respective branches is accelerated until the working pressure 
is re-established within the appliance. The excess of pressure 
on the main under throttling is then released, and will act as a 
reserve in meeting the extra tax, thus reducing the temporary 
disturbance in the flow to other branches. 

All these effects, due to variation of load and to throttling, 
as they occur with high pressure steam distribution for heating, 
have bearing on the final pressure at the point of delivery rather 
than on the amount of steam actually discharged. But, as the 
final pressure would be greatest under light load, when least 
needed, it becomes necessary to regulate the initial pressure to 
meet the demand. For these reasons the ideal theoretical method 
of reducing the pressure altogether by friction in transit is rarely 
feasible in practice, and may be approached only for long runs of 
mains without branches. The reducing valve at the individual 
apparatus which marks the end of the line, would in reality have 
the function of a regulator, to take care of such fluctuations in 
the final pressure as are caused by the variant flow. 

Application of Chart V. — To apply the chart, it is advisable 
to work up a schedule from the plan of piping on hand of which 
the quantity carried in all parts of the system can be figured and 
corrected for heat losses. Such a schedule should give all lengths 
to scale, indicate the features of obstruction and present, in 
general, all the factors entering the calculation. 

As a rule it is necessary to use the chart for approximation 
on hand of the quantities without taking into account the 
losses in transit. For a working pressure of 120 lb. per square 
inch, for instance, the nearest size for 300 h. p. or 10,000 lb. of 
steam may be found between the intersection of the slanting 
lines of 100 and 150 lb. with those of weight or B. t. u. For 
long runs, or when the initial pressure is to be kept up, the next 
larger pipe, 5 in. should be assumed, while in the opposite case 
the next smaller size would be indicated. 

The heat losses in transit should then be estimated on hand 
of the preliminary sizes, according to the class of insulation and 



76 THE FLOW OF STEAM 

disposition, and the quantities corrected for all parts of a system 
before the pressure losses are determined. The latter may be 
obtained by the other part of the chart, starting at the end of the 
line and adding up the items for friction and obstruction from 
junction to junction for each run of even quantity and diameter. 
If the quantity decreases materially by condensation the mean 
value should be taken as a basis. According to the nature of 
the problem, the pipe sizes and pressure losses may have to be 
modified in order to effect equalization of pressure at all points 
of delivery, or to bring the total drop within a desired limit. 
The example below will further illustrate the method of 
procedure. 

Example of High -pressure Steam Distribution. — The case illus- 
trated by Fig. 16 is a central heating station in which high- 



, , Mains between buildings insulated 


\5'4jfZ00OOO 
400DOOo\r^L3'''^-^^^^^ 


\ in underground conduits 




Xe"/ lb pressure 




^300000 




^^^mg)j5//! 


J^^^_____s=r==^ 


^' 


60000-^:^^^350000 ?i 
38. 5 lb (ll^k:^^''''''^'^'^^' 


^.^—--^^^^ 








/FRdieF 40000 - ^ - / lb. loss 






/pZSBOOOO 
// 3'//M3in 






Heat loss by convection 575 ■ 
" gain " friction .185 > 


^ LOS '100 =60400 B.fu 


•^' II '58000 " 


/■ 3 ' tiain 


\ tteaf loss by convection ZOO • 


' 915 'too =18300 B.tu 


1 " gain " friction .185 ' 


<^' 3.5 -13600 .. 


// 


Hea f loss by convection 90 ^ 


'.6ZZ'IOO= 5600 B.tu 


//■ Z" tiain 


" gam •> friction -185' 


<ff.5.5= 6900 " 


^1350000 






m^-^=^::m)34.7lb. Sca/e m net 








mo 





Fig. 16. — Example of high-pressure steam distribution for heating. 
Initial pressure 50 lb. per sq. in. 



pressure is carried for a laundry near the boiler house, but 
which otherwise represents a simple problem of transmitting 
heat to various appliances and apparatus for a considerable 
distance. The working pressure at the boilers is 50 lb. per 
square inch, the highest final pressure required at the buildings 
is 10 lb. for certain fixtures. A drop of 20 lb. seemed not only 
permissible, but also desirable, in view of reducing pipe sizes 
and furnishing dry steam. It would still leave a fair margin 
for service at lower initial pressure, when the friction loss is 



HIGH-PRESSURE STEAM DISTRIBUTION 77 

greater, also for reheating when less than 10 lb. final pressure 
will suffice. 

A3 1/2 in. main closely approximates these conditions. The 
heat developed by friction is nearly as large as the loss in transit, 
though it will not assure dry steam. This would only be obtained 
with a 3 in. pipe, which, however, reduces the pressure of delivery 
beyond a desirable margin. The pressure drop to the various 
branches is equalized as near as desirable. Reducing valves 
are used to permit a higher-pressure for various steam fixtures, 
and to graduate the pressure for heating the buildings according 
to the need. 

Owing to the heat developed by friction, the quantities to 
be carried by the mains would not be materially increased 
through the losses in transit, except for the dry returns, the 
condensation in which must be added to the tax on the line. 
The relief, which connects the supply to a dry return main where 
shown, without a trap, is sized to pass sufficient steam to make 
up the condensation and equalize the system as far as possible. 
Theoretically, the pressure loss through this relief should equal 
that through the supply main, apparatus, and returns beyond 
that point. This will prevent short circuiting or back pressure 
in the returns, and at the same time avoid excessive suction 
through condensing effect, which might disturb the water level 
at the lower end of the line. 



CHAPTER VII 
LOW-PRESSURE STEAM DISTRIBUTION 

Charts VI. and VIL — Of the two charts presented^ that for 5 
lb. pressure covers, in general, the field of heating by live steam 
at moderate pressure, while that for 1 lb. is intended for problems 
where distribution must be effected with the least drop in poten- 
tial, at or near atmospheric pressure, that is, for heating by ex- 
haust steam and for high class work generally. 

The diagrams for approximate sizing simply chart the relations 
of quantity and velocity for the commercial sizes of standard 
weight iron piping, with slanting lines for different rates of 
pressure loss, for which a pipe system may be proportioned tenta- 
tively, or for purposes of estimating. 

The quantities in both charts are stated in B. t. u. per hour, 
which is the generally accepted measure for estimating the heat 
transmission in buildings and emission or efficiency of heating 
surfaces. The B. t. u. as charted are based on the latent heat 
of the steam. The corresponding weight and volume can be 
found, if desired, on the table of properties. The true velocities 
may be read from either chart for any amount of heat and for all 
pipe sizes. The pressure losses are charted in pounds per square 
foot in place of the customary pounds per square inch since the 
various items of the calculation would be very small fractions of 
the latter unit. The pressure losses dealt with in problems of 
equalization have no direct relation to the working pressure 
carried. Hence there is no disadvantage in using another unit 
of measure. The total pressure differences from boiler to heat- 
ing surfaces, for which it is recommended to equalize a system 
are stated as a guide for various conditions. The data for esti- 
mating heat losses are added, with a general statement concern- 
ing corrections and allowances. 

Outline of the Problem. — Successful application of these charts 
depends again on familiarity with the factors entering into play, 
which can only be acquired by a study of the movements of the 
fluid under the widely different conditions presented by the 
various methods of piping. 

78 



T 

F 

t 

S1 

t\ 
m 



th 



CO 



Approximsfe S> 

6 1 e 9 10 



CHART VI 

LOW-PRESSURE STEAM 



THROUGH STANDARD WEIGHT IRON PIPES 



Pressure in lb. per sq.ft. to c 



( friction py = .03X.0257— jTifi- 
" '■ " " reaistanceof obstruction Pf = . 05 xl.07r—-. 

" " " create velocity p, = .05—. 

Total pressure for equalization P =P,-\-P,-\-p,. 

For two-pipe systems assume /'=S to 10 lb. per sq.ft. according to distance. 
" one-pipe systems assume P =4 to S lb. per sq.ft. according to distance. 
Static head in ins. viaXer H = .imP,. P.=^P nllowing for relie;itiiin. 



The B.t.u t 



1 should include tbe b 



Id be included for one-half of the length only in order to olilam 
'Blue for V as mean velocity for the run to be figured, 
lowance should he made for static head" under reheating when 
1 in heating surfaces is accelerated by forced wat«r or air circulaiion. 




LOW-PRESSURE STEAM DISTRIBUTION 79 

The flow of steam within an apparatus is governed partly by 
the condensing capacity of the several appliances, and partly 
by the carrying capacity of the pipes. These factors are inter- 
dependent to a greater or lesser extent. In a closed system, 
with all the air expelled, the pressure lost in distribution will 
bear on delivery only through the slight variations in steam tem- 
perature that may be involved. In any apparatus with fair cir- 
culation these temperature variations would affect the heat 
emission by a very small percentage only. With an open system, 
on the contrary, the volume delivered depends rather on the net 
pressure at the point of discharge, which may be the excess over 
the atmosphere, or whatever back pressure or vacuum is to be 
met. When operating under such low margin, the resistance of 
the pipe system will naturally bear on this final head available, 
which is the velocity head governing the delivery. Equalization 
of pressure losses is therefore essential to proper distribution in 
this class of apparatus. In practice, the closed or sealed system 
is never air tight or perfect in that sense. The actual situation is 
generally somewhere between the two possible extremes out- 
lined, since the necessity for removing air, no matter how it may 
be done, will open any apparatus to an extent, either, to the 
atmosphere, or to other influences affecting the net pressure and 
final discharge. To secure proper distribution it is always ad- 
visable, therefore, to assume the w^orst condition and to design 
the pipe system for equal pressure losses up to the ends of indi- 
vidual branches. How far it will pay to carry this equalization 
depends on the method of piping to be used, on the desirability 
of central or individual regulation of heat, and various other 
factors. 

Central regulation, as far as it is feasible with steam heat, can 
only be affected by a general lowering or raising of the absolute 
static pressure within the heating surfaces. The pipe S3^stem 
and appliances of an apparatus that will permit this should be a 
unit, practically closed to the outer air so that any pressure may 
be carried, from that necessary for distribution up to the limit 
set for the maximum heating capacity. As previously demon- 
strated, distribution is not materially affected by variations in 
boiler pressure, and it is proper to base calculations on the maxi- 
mum flow at the highest tension permissible, under a certain 
pressure loss. But in order to gain the full range of tempera- 
tures, distribution should take place at the smallest drop that 



80 THE FLOW OF STEAM 

can be evenly maintained up to all points of delivery. If the 
means of expelling air assure fair conditions, the equalization 
need not be carried to a small fraction. But inasmuch as the 
losses increase about as the square of the volume of steam passing- 
through the mains, which will often deviate considerably from 
the volume condensed within the appliances proper, according to 
the method of piping, it is necessary for even a fair degree of 
equalization to consider the system to be used. This should be 
done especially in reference to features which involve extra tax 
on mains and branches aside from condensation in transit. Dry 
returns, drips, reliefs and similar appendages or dead ends, for 
instance, will increase the volume to be carried, as also the 
variant means for removal of air and other special devices, 
which may entail a certain leakage. 

Individual hand regulation by throttling devices, which give 
control over the admission of steam to the heating surfaces, 
requires a constant final pressure at the point of delivery. This 
must be closely equalized by friction or by special means of ad- 
justing the pressure drop, as a vital condition to fair distribution. 
The returns of such a system are assumed to be open to the 
atmosphere, and the pressure carried within the supply piping and 
boiler is merely that necessary for distribution. An excess be- 
yond that would cause a waste of steam, which would have to 
be checked by further adjustment or by traps. While in a closed 
system condensation takes place throughout, an open one 
theoretically passes no steam to the returns, and the total amount 
carried, and bearing on the resistance to the flow, is that con- 
densed within radiation and supply pipes only. 

The calculation of the distributing pipes will thus be modified 
according to the necessity for close equalization, and according 
to the excess volume to be moved which affects the loss of pres- 
sure and delivery. From these points of view the various 
methods of piping may be divided into three principal classes 
illustrated by Figs. 17, 18 and 19, representing respectively the 
wet return, the dry return and the open return idea. The 
bearing on the calculation of single or separate lines for steam 
and condensation, and of special devices for accelerating circu- 
lation, which may be applied with any or all of the main classes, 
are subordinate in importance from these view points, but should 
be considered in connection with each case. The effects of 
throttling, or the occasional shutting of branches, and of varia- 



LOW-PRESSURE STEAM DISTRIBUTION 81 



CljE 



L 




Fig. 17. — Steam distribution with wet returns, with or without vacuum or air lines, with 
single or double piping to individual radiators. 



e 



€ 



3L 



^Q 



-9 



Fig. 18. — Steam distribution with dry returns, with or without vacuum or returns or air 
lines, with single or double piping to risers and radiators. 




Fig. 19. — Steam distribution with open returns, with adjustable 
valves only. 



82 THE FLOW OF STEAM 

tions in working pressure differ somewhat with the method of 
piping, though not radically. They bear on distribution in a 
similar way as pointed out for high-pressure steam. 

Application of Charts VI. and VII. — The method of applying 
the charts is the same for any system of distribution and .of 
regulation. It is always advisable to work out a schedule on 
the basis of the plans, in order to get a clear and comprehensive 
view of the situation in regard to the various points to be con- 
sidered and in order to decide how far it w^ill pay to carry 
equalization. The quantities and other data should be entered, 
the piping sized tentatively, and the heat losses up to and beyond 
the heat emitting appliances estimated and added according to 
the nature of the case, as will be outlined for each of the principal 
modes of piping. Allowances should be noted at the same time 
where condensation materially decreases the volume. 

Figuring accurately, the quantity for any run of even diameter 
should include only one-half of its own condensation, but unless 
such losses are a considerable part of the whole volume passing 
that run, it is not necessary to split these individual items, 
as they are relatively small as a rule and the result is hardly 
affected whether the total is taken as a basis, or the mean 
quantity. 

The final calculation of resistance heads may then be carried 
out with greater or less approximation, as the situation may 
demand. As a rule, it will be found convenient to establish and 
write down simply the losses, or differences of pressure from the 
boiler forward, from junction to junction, for all runs of even 
quantity and diameter. If equalization appears impracticable 
owing to high resistance between junctions, which would re- 
sult in excessive differentiation between the branches at the 
near and far ends of the main, the size of the latter should be 
increased. In general, the ways and means to effect equalization 
are the same as indicated in the chapters for the flow of water. 

For sizing returns, the charts give also a convenient way 
of proportioning, which may be modified, however, according 
to the method of piping used^ and is explained in connection 
with the same. 

The proportions of air lines are also touched upon in dealing 
with the various systems. 

Wet Return System. — Fig. 17 illustrates a pipe system with a 
wet, or sealed return. Steam fills the entire system down to the 



CHART VII 

LOW-PRESSURE STEAM 

At 1 lb. per sq.lD. Mean Pressure 

THROUGH STANDARD WEIGHT IRON PIPES 



atevelocitypr = .04— . 

P = 6 to 12 lb. per sq.ft. according to distance, 
■pipe systems asume /*=4to S lb. per sq.ft. according to distance, 
a vapor systems assume P =4 to 8 lb. per sq.ft. according to distance, 
ead in ins. water H = .192P,. P,=4P allowing for reheating. 



Approximate Si. 



Total pressure for cqualizatic 
For two-pipe ^tems assume 



J pipes per sq.ft. of pipe surface, 100 B.t.u. per hi 

tical pipes in rooms per sq.ft. of pipe surface. 300 B.t.u. per hi 
izontal pipes in rooms per sq.ft. of pipe surface. 400 B.t.u. per li 

Corrections 
posed piping and long distances of even diameter the heat lo 
ou]d be included for one-half of the length only in order to ol 
t value for r as mean velocity for the run to be figured. 

ade for static head under reheating ' 
heating surfaces is accelerated by forced water or air circula 



More allowance should 



Qrn ^nd Return Pipes, ai -Siaf^ 
^40 30 60 70 60 



facton^ of Resistance to the F~lo^ for 




aer aq.in. tiean Pressure (iS.T lbs. absolutej in !000 Btu- per hour Includina Loss in Transit 



LOW-PRESSURE STEAM DISTRIBUTION 83 

water line. The bulk of it condenses within the appliances, but 
a considerable part is always dropped in transit and in the dry 
portions of returns and reliefs. The size of steam supply pipes 
at a given point is clearly to be based on the volume passing that 
point, or on the total condensation beyond it. The steam con- 
densed in exposed return risers, for instance, should be included 
in the volume passing into a radiator, and added, with the losses 
in the supply pipes, to the amount of steam passing through the 
mains. 

For a systematic calculation of a distributing system the pipe 
schedule should show the general situation in respect to heat 
losses ahead or beyond appliances, based on the preliminary 
sizes, as well as the length of runs and items of resistance to the 
flow. The aim should be to establish as near as possible the true 
quantities, or approximately the volumes, carried in each part of 
the system. The resistances for each run of even diameter and 
velocity, from the boiler up to the point of discharge may then 
be determined with sufficient assurance from the charts and 
equalized by selection of proper sizes. 

As stated in a general way, the drop of pressure in the main 
itself should be kept down so that the individual connection 
furthest from the boiler will not have to be excessively large in 
order to come within the desired limit, while the first connection 
should not figure much less than the customary size in order to 
make up the same total pressure drop. If this total is equalized 
in this way, the static heads h^, h^ and hg or the water lines in the 
returns will be on a level. The height of these heads above the 
water line in the boiler will then correspond to the loss of pressure 
by friction and obstruction up to the appliances, provided, the 
return pipes offer no appreciable resistance. Likewise, the 
static heads hg and hg in the relief pipes indicate the pressure 
losses in the mains up to the points d and e. It is not necessary 
to equalize the static head in these sealed reliefs, since the 
water cannot rise higher in them than in the sealed returns from 
appliances, but it will pay to establish these heights where the 
steam mains are placed near the water line. For the same 
reasons the pressure drop permissible in a sealed return apparatus 
is limited sometimes by the level of heating surfaces. Mains 
and appliances should be located well above the calculated 
normal water line in the return since the pressure loss and the 
static head will be much greater under the extra tax on the pipes 



84 THE FLOW OF STEAM 

when heating up. With the volume of steam temporarily 
doubled, for example, the water will rise to four times its regular 
height, hence a very liberal margin should be provided beyond 
the calculated head. A fair height for the mains above the 
water line in boilers is given by the simple formula H = .192 Pg, 
taking Ps = 4P, or roughly four times the total pressure loss in 
pounds per square foot up to the relief or return pipe in question. 

With single pipe lines carrying all their condensation against 
the steam it is advisable to allow for the extra resistance by 
doubling the losses found by chart for these runs, thus calling 
for larger sizes to obtain the same drop of pressure. 

As a rule, close equalization is not essential for a sealed return 
system, but it is advisable to compute the pressure losses at 
least approximately, in order to render account of the differences 
in water level created, and, as previously pointed out, with the 
idea of better general regulation, as well as simultaneous 
reheating. 

Theoretically, the method of removing air, whether by hand, 
automatic valves, or by suction in various forms, should make 
no difference on the flow of the steam in the supply piping, 
if the air is removed without allowing steam to escape. 
The air valve is presumed to be closed whenever the heating 
surface is in full action, hence there should be no extra volume 
of steam passing beyond, and no increased tax on the mains. 
The flow of steam and pressure drop are increased only when 
vacuum is turned on during reheating, or through leakage. If 
evenly distributed, the increased net pressure created may then be 
assumed to make up the extra pressure loss due to greater 
volume. 

The free opening of ordinary automatic air vents bears on the 
pressure loss during the period of reheating, in so far as a rapid 
escape of air will accelerate the condensation, but the discharge 
through the valves depends again upon the pressure available 
for expelling the air, which may be affected by back pressure 
through the air lines. For heating systems working under very 
slight pressure difference, especially when exhaust steam is being 
utilized, under vacuum or not, it is desirable, therefore, to 
equalize, approximately, the back-pressure produced by a system 
of vents. It would be impracticable to estimate the volumes 
of air, and, in any event, to carry out a detailed calculation, but 
a fair equalization should be secured by maintaining a certain 



LOW-PRESSURE STEAM DISTRIBUTION 85 

proportion to the steam supply pipes. If, for instance, air lines 
are sized for one-fourth of the diameter of the corresponding 
steam supply pipes, they will generally prove to be ample, and 
bear out the best practice. It is recommended also to size the air 
valves accordingly and to use larger patterns for appliances calling 
for larger steam connections. This rule would tend also toward 
larger air lines and valves on long runs of mains, from which 
more air is to be expelled, since long runs will always call for 
larger sizes, if properly calculated. 

In a wet return system, with each drip from the individual 
appliances sealed, very little steam is usually carried in the return 
piping above the water line, as it represents only the condensa- 
tion in the dry portions. Whatever the amount may be, it will 
rarely enter as a factor in sizing the return pipes, the idea being 
to make them large enough to practically eliminate any addi- 
tional loss of pressure on all branches beyond the point of de- 
livery, at which the supply pipes are equalized. Since it would 
not pay to investigate in each case, or to calculate whether the 
friction head in the wet portions exceeds a certain limit, a general 
rule of proportioning may be figured out which will keep the 
resistance of the water at or below a certain ratio to that of the 
steam. This ratio would naturally maintain also for the period 
of reheating, when the amount of water increases at the same 
rate as the volume of steam and would, to a degree, equalize 
the losses in the returns or neutralize their effect. 

Since the volume of the condensation is only about .0007 
times that of the steam at 1 lb. pressure, the resistance head, in 
a wet return, for a uniform proportion of one-half of the diam- 
eter of the corresponding steam supply pipes figures only about 
1/20 of that within the steam lines. This pressure loss in the 
return should be added to the total in the steam mains, but as it 
is nearly alike for all branches, it can hardly bear on distribution 
and may be neglected altogether for purposes of equalization. 

For practical reasons, this proportion recommended is not 
applicable to the smallest branches. Hence the lines for sizing 
the returns on the approximation diagram will be found to gradu- 
ate them so as to make the minimum size 1/2 in. This relative 
increase for the smaller piping brings the pressure losses down 
still further and makes it inappreciable, at least for pipes running 
full, without carrying steam. 

If the sizes of the steam lines are materially changed by the 



86 THE FLOW OF STEAM 

final calculation, it will be proper to correct the returns to con- 
form to the rule of half diameter, but discretion may be used in 
such cases. 

Example of a Wet Return System. — Fig. 20 is a working 
schedule of a typical low-pressure steam heating apparatus on the 
two-pipe plan, with sealed returns. The system includes direct 
and indirect heating surfaces emitting the maximum heat 
required at a pressure of 1 lb. per square inch, while distributing 
evenly at the least practicable excess above the atmosphere. 

The tax on the mains is not greatly in excess of the total 
for the heating surfaces, except for a few exposed rising lines and 
their returns. Aside from the latter, the condensation in transit 
amounts to only 40,000 B. t. u. or less than 10 per cent, of the 
net total. With moderate sizes for the mains, corresponding 
practically to those given by the approximation diagram, it has 
been possible to equalize the losses in branches, risers and con- 
nections, without resorting to undesirably small or large connec- 
tions, at a pressure drop of about 7 lb. per square foot, or only 
about .05 lb. per square inch. If the automatic air vents are in 
working order, this pipe system will circulate throughout before 
any pressure is recorded by an ordinary gauge, and could be 
operated as a so-called vapor system. The equalization might 
be made still closer by increases or reductions of sizes for parts 
of connections, but the effect on the heat distribution would 
hardly be appreciable. The ample pipe sizes resulting from the 
small pressure drop for distribution at normal operation provide 
a safe margin for extra tax and will permit rapid reheating with- 
out fear of disturbance. The total pressure loss under reheating 
4 P = 28 lb. per square foot may in this case raise the water line 
in the extreme end of the system by .192X28 = 5.4 in. There 
would be no danger, therefore, of any water backing up into the 
stacks, if the latter are placed ebout 6 in. above the water line in 
boiler. Check valves are not needed on the returns when the 
possible pressure losses are known and taken care of, nor is 
water likely to be entrained even with a flow considerably in 
excess of that for regular service, because of the moderate steam 
velocities necessary for equalization. In cases where such lia- 
bility exists, due to peculiarities of boiler design or other causes, 
it would be advantageous to enlarge the main line up to the first 
turn or the first branch, thus reducing the initial velocity still 
further and the pressure drop throughout. 



LOW-PRESSURE STEAM DISTRIBUTION 



All steam and return pipes in cellar insulated 

Piping upstairs not insulated but Furred m or concealed 
except risers marked (R}as tieatmq surface 

Return mains-sealed 

Gate valves used on mamsand branches 
-IZJOO Globe " " " heatinqsurfaces 
-5000 Close elbows used ttirougtiout 




Fig. 20. — Example of low-pressure steam heating at 1 lb. pressure 
Wet returns — two-pipe distribution. 



88 THE FLOW OF STEAM 

Dry Return System. — The dry return idea, as generally under- 
stood, differs from the wet return only through the disposition of 
the water seals, which are placed on the mains, instead of being 
put on the individual branches. The essential feature to be con- 
sidered is the possibility that steam may pass from the supply 
pipes into the returns and back up through appliances, thus giv- 
ing opportunities for short-circuits which do not exist with a 
separate water seal for each individual branch. Strictly speak- 
ing, any wet return apparatus with double risers to several 
stories is a mixture of the two systems, unless the condensation 
from each radiator, on all stories, is carried in separate lines, 
sealed before entering the main. Return risers with several 
radiators should, in fact, be calculated as dry returns. 

The equalization of such a system, in order to assure smooth, 
even circulation, should be carried out with the idea of avoiding 
short circuits. Referring again to Fig. 18, the pressure losses, 
theoretically, should be calculated to be equal for the runs a-b- 
1-m and a-b-c-d-k-1-m and a-b-c-d-e-f-g-h-i-k-1-m. In 
other words, whatever steam passes through branches and re- 
liefs into the dry return mains at 1, k, i, and h, should be no more 
than necessary to replace condensation in the same and move 
toward the boiler. An excess entering at 1, and passing up 
through k, d or i, h would run against the condensation and may 
disturb drainage. The quantities of steam necessary to keep 
the return mains filled, especially the non-insulated portions, 
will thus become a factor, not only in sizing the relief pipes, 
which should pass that steam under a certain head, but also in 
the computation of the resistances for the supply piping. The 
heat emitted by these mains adds often materially to the tax on 
the pipe system. Bare return risers, for instance, should always 
be figured as heating surface, and the steam included in the 
volume passing into the nearest radiator above. Return risers 
should thus be filled through the radiator connections above 
them, while the horizontal runs are naturally taken care of in the 
same way through the reliefs. 

Unless a dry return apparatus is proportioned on this principle, 
there is liable to be a counter flow of steam in some parts of the 
system. At the period of reheating this counter flow of 
steam is increased and is liable to meet the first condensation, 
which is always cold. When meeting cold water, this steam is 
condensed at a very rapid rate and increases the tax on the 



LOW-PRESSURE STEAM DISTRIBUTION 89 

mains still further ut a critical time, when the system is already 
taxed beyond the normal. The disturbances often resulting 
from this cause have made dry return mains unpopular. When 
correctly sized, dry mains can be used safely without artificial 
devices for drainage. 

The flow of steam within the dry returns, induced only by the 
condensation within the same, causes but a small part of the 
total pressure drop from a to m. Nearly all of the resistance is 
met in the runs up to the heating surfaces and up to the points 
k and h on the reliefs. It is not necessary, therefore, except 
under unusual conditions, to carry out the theoretical equaliza- 
tion down to the water line at m which indicates the total loss. 
The logical thing to do will be to equalize again up to the appliances 
only, but making full allowance for condensation in all dry re- 
turns and to reduce the losses in the latter to a point where they 
cannot become disturbing factors. Reliefs from main to main 
should be sized to present equal resistance as any other branch, 
for instance up to k and h, treating the portions of dry return 
mains to be filled as heating surfaces. 

It has been found in practice, that dry returns should be larger 
than wet returns. Proper calculation, taking full account of 
all the losses in transit, will result in the first place in appreciably 
larger steam mains. If the returns are then sized on the same 
proportion of 1/2 diameter, they will also be larger, but it will 
often be desirable to allow for the steam to be carried with the 
water. To what extent this is advisable depends, of course, 
on the individual case. While larger pipes will generally help, 
they will also increase the condensation. It is always better to 
treat each case on its merits, by proper equalization, that is, 
by increasing the sizes beyond one-half of the diameter of the 
steam pipe, wherever the resistance might become appreciable. 

Dry return mains may be used also with single rising lines, 
carrying steam and water. These should be computed in the 
same way, with reduced drop, as recommended in connection 
with a wet return main, except that the next relief should be 
proportioned so as to pass about the right amount of steam with 
the water. 

The method of air removal will bear on the flow in a dry 
return system in a similar way, as with sealed returns, if arranged 
through air valves on the appliances, and vice versa, the final 
pressure in radiators will affect the action of vents. Air lines 



90 THE FLOW OF STEAM 

may be proportioned accordingly on the same plan as recom- 
mended for the wet return system. 

If vacuum is applied, it can be made to act in this case 
through air lines or through the returns. No increase of flow 
can be counted upon, if the vacuum is automatically controlled at 
the return ends of radiators. No decrease in pipe sizes seems 
justified, therefore, on the assumption that the vacuum will help 
the flow, if the air vents will shut properly, as they should. 
Under regular operation the flow will again be governed by the 
amount of steam condensed. Where it is desirable to reduce the 
working pressure below the atmospheric, a continuous leakage is 
necessary, and the return ends of radiators are to be left open 
to the suction. The extra volume of steam passing will then 
depend principally upon the surplus of steam available or to be 
condensed, and the capacity of the jet or other device for dis- 
posing of it, and creating the vacuum. Allowing for such a 
surplus, which puts an additional tax on the steam mains, and 
considering also that the volumes and friction losses are still 
further increased under lower mean pressure, it is best not to 
reduce sizes, even though a larger pressure drop can be secured 
under vacuum. When the vacuum must be created by 
motive power in one form or another it is naturally advantageous 
to keep down resistances. It seems proper, in any event, to 
calculate for the pressure that is likely to be carried in extreme 
weather, and effect equalization under a moderate drop between 
the boiler or reducing valve and radiators. The return mains 
likewise should not be reduced on account of the use of vacuum, 
inasmuch as the tax on them may be materially increased 
thereby, and an effective transmission and equalization of the 
vacuum itself is highly desirable. 

Example of a Dry Return System. — The pipe schedule illus- 
trated by Fig. 21 shows a low-pressure steam heating apparatus 
for a bank building that presented somewhat unusual conditions. 
Dry returns were necessary in some parts to avoid pipes on the 
floor or in trenches, and in other parts in order to utilize them 
as heating surface. The tempering coil returns are kept dry to 
avoid backing of the water from one section into another under 
extreme condensation. The individual return branches thus 
communicate, but the main branches unite below the water 
line and are separated. The total tax on the system is 1,611,000 
B.t.u., while the heating surfaces proper call for only 1,359,600 



LOW-PRESSURE STEAM DISTRIBUTION 



91 



Distributing system equalized For a pre 
loss approximating 8.5 Ibs.persq. Ft ^ 

i J 




\^ /-har e dry r e furrr ^ j 

All steam and return pipes insulated, unless otherwise marl<ed 
Gate valves used on mains, brandies and temp, coils 
Globe " " " radiator connections 
Sweep elbows used on mains and close elbows on connections 

Sca/e in' reef 

Fig. 21 — Example of low-pressure steam heating at 1 lb pressure. 
Dry return — two-pipe distribution. 



7 



'^ 



92 THE FLOW OF STEAM 

B.t.u. The condensation in transit figures therefore 251,400 
B. t. u. or over 18 per cent, of the heat to be transmitted. Of 
this latter amount the dry returns, partly utilized, call for 
94,300 B.t.u., causing a very decided extra resistance in some 
portions of the system. Even if all were insulated, they would 
be an appreciable factor in the calculation. 

The mains figure somewhat larger than the nearest sizes from 
the approximation table. The equalization is not as close as in 
the preceding example, but keeping within 10 per cent, of the 
average pressure loss of 8.5 lb. per square foot. These dis- 
crepancies could only have been reduced by further increase of 
mains or by reductions of sizes in odd places. As it is, the pipe 
system assures a very fair distribution of the heat and responds 
quickly, without noise, while steam is being raised. 

Although the calculation of pressure losses in the connections 
to tempering coils is necessarily problematical, owing to the 
fluctuations and uncertain condensing capacity of the several 
sections under automatic control, it will pay to carry it out, as 
near as practicable, to avoid excessive pressure differences 
between the several sections, which would cause disturbance 
in the returns. The ample sizes in which such a calculation 
invariably results, w^ill also neturalize the effect on the other 
parts of the system of the sudden flow to coils under the operation 
of automatic regulators. 

The reliefs are sized to pass sufficient steam to fill the sections 
of returns to the nearest relief, or to the water seal below, at a 
pressure drop making up as nearly as practicable the total for 
equalization. These reliefs are desirable especially where all 
radiation may be shut at times and cannot be depended upon to 
pass any steam to the return main. The resulting vacuum may, 
under certain conditions, disturb the water line. 

Example of Low-pressure Steam Heating at 5 lb. Pressure. — 
The schedule shown by Fig. 22 represents a typical one-pipe 
system, with returns for the horizontal mains only. A part of 
the latter is dry, the other part is sealed. The total tax on the 
boiler is 203,000 B. t. u. while the heat emission of the radiators 
aggregates only 166,000 B. t. u. The balance of 37,000 B. t. u. 
is mainly heat from the risers which is generally utilized in this 
class of work, but not always duly taken into account when 
sizing the pipes. It represents, in this case, 22 1/2 per cent, of 
the net tax and increases the pressure loss in the mains by 



LOW-PRESSURE STEAM DISTRIBUTION 93 




V^ , y-49000 
l^*°VlOOO 



Mains and branches in cellar insulafed 
Risers CKposed as heating surface 
Connections to radiators under Floors, 

but not insulated 
Gate valves used on mains 
Globe " " " radiators. 
Close elbows used throughout 



'Pressure loss in single pipes carrying condensation 
against the riow of steam IS doubled System is 
equalized for about 4 lb persq. ft 



Fig. 22. — ^Example of low-pressure steam heating at 5 lb. pressure. 
One-pipe system. 



94 THE FLOW OF STEAM 

nearly 50 per cent., thus becoming a decided factor in the 
calculation. 

The equalization is carried out to within 10 per cent, of the 
stated total drop of 4 lb. per square foot without excessive sizes 
of mains, and without reducing the area of near branches beyond 
a point at which the condensation would not flow freely against 
the steam. A safe limit in this respect is given by the line of 
pressure losses for one-pipe systems on the approximation table, 
which should be considered as giving the smallest size advisable 
for single connection draining backward. If the size of the 
nearest branch, thus determined, makes the pressure drop much 
smaller than desired, it is best to modify the sizes of the main, 
with the idea of reducing the losses between junctions, or deliber- 
ately to take off the first branch at a point further away from 
the boiler, thereby increasing its length and total resistance. 
Each problem should be studied individually in order to find the 
best and most practical means to effect fair equalization. 

With a sealed return main the circulation will always be more 
positive, or under better control. This will be apparent when it is 
attempted to figure the sizes of the reliefs from rising lines dis- 
charging into a dry return. Such relief pipes must pass the 
condensation from the riser and all its heating surfaces, also the 
steam that is needed to fill the return main down to the water 
seal. It is practically impossible to calculate the pressure drop 
in the relief under these conditions and it will be best to pro- 
portion them as returns, keeping down the sizes of the reliefs 
near the boiler in order to prevent a counterflow of steam to 
those further away. Thus the return and relief on the first 
riser on the dry end of the system in Fig. 22 is made only 1 in., 
while under usual conditions 11/4 in. would be the proper size. 
Owing to the greater tendency for the steam to rush through at 
this point, there will be no difficulty in draining by the 1 in. 
pipe provided. 

A one-pipe distributing system computed on this plan can be 
made to circulate as well as any arrangement with double piping 
and other improvements, but if properly carried out, the saving 
in first expense will not be as great as is generally assumed, 
since the pipe sizes undoubtedly should be more liberal, even at 
higher boiler pressure, to allow for the extra resistance of the 
water flowing against steam. 

The Open Return System. — Returns and air lines combined, 



LOW-PRESSURE STEAM DISTRIBUTION 95 

and open to atmospheric pressure, are only feasible when the 
discharge of steam through each branch is restricted to the 
amount which the appliance will condense. This restriction 
may be obtained either through the resistance to the flow pre- 
sented by the boiler outlets, piping, valves and heating surfaces, 
or by special throttling devices permitting adjustment and gradu- 
ated control of the volume for a stated initial pressure. The 
latter may be lowered for purposes of a general reduction, or 
central regulation of the heat, but must not be exceeded, lest 
steam be wasted through the open returns. Again, the full 
working pressure must not overbalance a water column limited 
to the height of the return main above the water level in the 
boiler, as indicated by H on Fig. 19. Higher initial pressure 
would seal the return, prevent the free escape of the air and de- 
stroy the possibility of graduating control over the steam at the 
appliances, which is the principal reason for using this method. 

Reliefs from the steam mains are to be separated from the 
returns from heating surfaces, or they may be trapped to pre- 
vent discharge of steam. The static head h2 in the relief cor- 
responds to the pressure drop in the steam main, w^hile the head 
hg in a trap is the difference between H and the loss of head up 
to point d. These seals must be carried low enough to allow 
for this. 

When properly adjusted, the return system of such an appara- 
tus will carry only water and air. The volume of steam entering 
into calculation is, therefore, strictly that condensed by the 
heating surfaces and the supply piping. The loss in transit, 
moreover, is liable to be smaller in a well designed open return 
system than in a closed one, since it is desirable to insulate the 
steam supply pipes thoroughly for better control over the flow. 

Successful hand regulation by graduation valves depends upon 
close regulation of the working pressure and also upon close 
equalization of the pressure losses. Theoretically, the pressure 
drop should be calculated from the boiler up to the individual 
or common outlets to the atmosphere, usually a stand pipe at 
the end of the return main, making the total for circuit a-b-b^- 
ba-i-k equal to the total for a-b-c-d-e-ei-e2-f-g-h-i-k. The 
resistances in the combined return and air lines, or what might be 
called the back-pressure on the radiators, would be difficult to 
estimate. It_ is best to proportion the piping again to prac- 
tically eliminate its effect on the flow by liberal and consistent 



96 THE FLOW OF STEAM 

sizes of returns. The question will then arise whether the 
system should be equalized up to the controlling valves at points 
bi and e^ or up to the return ends of appliances b2 and e^. In the 
former case, if an equal pressure is actually maintained behind 
each valve, the discharge through the same must still be ad- 
justed to obtain the right resistance for the valve and the appli- 
ance itself. In the latter event, the resistance of the graduating 
valve and the radiator itself is included in the total pressure 
drop, and no adjustment would be necessary, in theory, if the 
factors of resistance for these valves and other parts of the dis- 
tributing system were accurately known, and the plant carefully 
calculated and executed. The uncertain elements in the com- 
putation and construction make it necessary to depend on ad- 
justments in either case, but that process is made easier and 
favors more accurate graduation if aided by previous calculation 
as far as possible and leaving the least amount of adjusting to 
be done by the fitter. 

The factors of obstruction for the graduating valves differ 
greatly with the type, design and the full net opening, which 
is often much less than that of the nominal pipe size. According 
to Zyka's experiments^ on the discharge capacity of such valves 
under various heads, the factors based on actual velocity at 
smallest area would figure about r = 2, or equal to that for a 
straightway globe valve, or for an angle valve with radiator. 
This includes the velocity head lost in discharge. The thin jet 
of steam issuing from a valve of this type probably represents 
about all the loss of motion taking place within the radiator 
itself, and unless the device used seems obstructive to an excep- 
tional degree, it will be safe to assume the same factor for radi- 
ator and valve combined, as given on the charts for ordinary 
connections. 

The effect of reduced working pressure and of throttling 
on the delivery is naturally greater with an open sys- 
tem than with other methods of piping, since the discharge 
is controlled entirely by the balance of pressure available at the 
valve, not by the condensing capacity, which regulates a closed 
system. An open apparatus, therefore, will have a smaller 
range of central regulation and the most accurate graduation 
under normal conditions is easily disturbed by throttling and 
variation of boiler pressure. For these reasons the claims for 

^ "Gesundheits Ingenieur, " Vol. xxix, No. 21. 



LOW-PRESSURE STEAM DISTRIBUTION 97 

graduated control are often disputed. Since a reasonably 
certain reduction of the discharge to a given fraction repre- 
senting say 3/4, 1/2 and 1/4 of the total heat is the essential 
feature and main advantage of the open return method, the 
endeavor should be to design the distributing system with a 
view to reducing the disturbing effects. This can be done, as 
previously pointed out, by liberal sized trunk lines, by elimi- 
nating as much as possible the uncertain factors that call for 
throttling, and by lessening the condensation in transit which 
is liable to vary, and to bear on the volume and resistances to 
an appreciable extent. 

The general procedure in calculating and equalizing an open 
return system is the same as outlined for the other modes of 
piping. With the quantities of heat scheduled closely, it will 
differ only in the degree to which equalization should be carried 
out. The total pressure loss permissible will be approximately 
equal to that for a closed system for the same structural dimen- 
sions. The total will define the working pressure above atmos- 
phere. In any case, the mean pressure to be taken as a basis 
for calculation is not likely to exceed 1 lb. and the diagram for 
that pressure will be found accurate enough. 

Example of an Open Return System. — The apparatus represented 

by the schedule (Fig. 23) will permit a water column of 4 ft. in 

the return at the boiler up to the level of the open overhead 

main, corresponding to a total pressure drop permissible of 

48 

= 1.73 lb. per square inch. Allowing for increased 

.192X144 ^ ^ ^ 

heat and friction losses in transit when heating up, the boiler 
pressure might safely be run up to about 1 lb. per square inch. 
The system is calculated with the view to obtaining the required 
discharge at each appliance by a close equalization of the pressure 
losses from the boiler to the radiators with the least amount of 
throttling. The initial boiler pressure therefore exceeds the at- 
mospheric only by the margin necessary to overcome the friction 
and local resistances, which in this case is made to approximate 5 
lb. per square foot to all points of delivery, and is a small frac- 
tion of that which the water column in the return will permit. 
The valves are of a type having nearly the full area of the pipe 
connection, so that the discharge velocity is moderate and not 
liable to cause noise. They contain the means for adjustment 
of the full opening to effect still closer equalization. The throt- 



98 



THE FLOW OF STEAM 




33000- 
10000 



44000- jj 



j|/2 1/4 

1 I.'.II R^oooo 




All piping insulated 
Gate valves used on mains 
Globe " ■■ " radiators 

Close elbows used throughout 



High wafer in open retur n 



4 ft 
Water line ■ in t>oiler 



Distributing system equalized For a 
pressure loss ofabout 5lbs.per sq. Ft 



Fig. 23. — Examples of low-pressure steam heating at 1 lb. pressure. 
Open return system — with adjustable steam valves. 



LOW-PRESSURE STEAM DISTRIBUTION 99 

tling incidental to this process will naturally raise the working 
pressure to an extent depending on the skill of the mechanic, 
but the plant can be made to circulate perfectly at very low 
pressure and might properly be termed a vapor heating appara- 
tus. Close regulation of the steam pressure is essential for the 
successful operation of such a system, since a slight increase will 
cause an escape of steam through the returns. If this be pre- 
vented by automatic trapping, an undue rise of pressure will 
affect the graduation to some extent, but will not cause any 
other disturbance, until the water column in. the return will 
seal the system and turn it into a wet return apparatus, poorly 
designed as such and liable to be noisy. A secondary condition 
for the successful operation of an open system is therefore a 
close and positive control over the initial or boiler pressure. 
Special devices are necessary to secure the proper results. 



THE FLOW OF AIR 

CHAPTER VIII 
THEORY OF THE FLOW 

Properties of Air. — The diagram of properties is presented for 
occasional reference to the weight of the air as the absolute 
quantity, the charts being based only on volume, which is the 
convenient measure, and sufficiently accurate in general prac- 
tice, with the corrections noted. 

The diagram also shows the influence of moisture on the 
volume, which increases rapidly at higher temperatures, and 
may become of importance in connection with drying problems. 
The weight of water that can be absorbed by air at different 
temperatures is given by a separate scale. This weight corre- 
sponds by no means to the difference in weight between dry and 
saturated air, because the volume increases with the percentage 
of moisture. 

The temperature variations enter frequently into the mecha- 
nical problems and are accordingly stated and incorporated in 
the charts used for calculating. 

The bearing of barometric pressure and altitude on pressure 
and power is appreciable and should really be taken into account 
under extreme conditions. Inasmuch as it is usually negligible 
and nearly always within the limits of error from other sources, 
the data has been omitted for the sake of simplicity. 

Friction in Conduits. — The general expression for the loss of 

vM . 
head by the friction of fluids in conduits Hf = f is applicable 

to air. The coefficient f naturally takes different values than 

those for water and steam owing to viscosity and nature of 

conduits. It varies also with the relation of internal and 

external friction, that is, upon the ratio of area to contact surface 

and its roughness. 

.217 
Weisbach gives the value f = — ~^^for air, derived from experi- 

V V 

ments. These seem to have been limited to very small tubes 
with smooth surfaces, and high velocities, entirely outside the 

100 



THEORY OF THE FLOW 



101 



Volume oFAJr per Ittaf Atmospheric Pressure. 29.S2 Mercury 
16.5 16 15.5 15 14.5 14 13.5 13 IZ.5 IZcu.R. 



3.5B.tu. 




J I I L 



.065 .07 .075 

Density, or Weight per cu. Ft at Atmospheric Pressure 
I I I I I II 1 11 I I M I I I I I I I I 



0851b. 



J L 



.008 .006 .004 .002 .001 .0005 

Weight oF Moisture Absorbed by leu. Ft oF Air to Saturation Point 

Diagram D. — Properties of air. 



.0001 lb. 



102 THE FLOW OF AIR 

range occurring in heating and ventilating practice. According 
to this formula the coefficient changes only with the velocity. 

Grashof finds f=.0135 + -^ :, — 7^ thus showing the 

dVv 

coefficient to vary both with diameter and velocity. 

Pelzer also recognizes these variations including them in his 

748 1 
formula for the loss of pressure Pf = w^''^ v^ 

10^ (^1-373 

Stockalper, as the results of his tests on tunnel ventilating work, 
gives fo)' cast iron pipe 6 in. to 8 in. diameter 



^ 785 1 /^ Iv 



being expressed in m/m water column. According to this 

formula the coefficient increases as the diameter decreases, but is 

not affected by the velocity of flow. 

Lorenz, as quoted by ^^Die Hiitte," stated the friction loss in 

lv2 
air pipes to be Pf = P.f — — ,wherein T and P are the mean 

absolute temperature and pressure in the conduit. The coeffici- 
ent of friction f is given for diameters ranging from 2 in. to 14 in. 
and is taken to apply at any velocity. 

Brabbee, operating on round sheet metal piping from 12 in. 
to 32 in. diameter, also used for tunnel ventilation, finds f 
practically constant for these sizes, at velocities ranging from 
10 ft. to 50 ft. per second. His value for f is obtained by a 
series of very thorough experiments and checks closely with the 
average of the values by twenty other authorities quoted by him.^ 

Taylor, as the outcome of his tests for the U. S. N.,^ agrees 
that f is practically constant for diameters from 12 in. to 27 in. 
and at velocities up to 100 ft. per second. 

Rietschel, experimenting for the Vulcan Iron Works,^ has 
compiled a table of values which shows f to vary both with cir- 
cumference and velocity. Intended to apply to ductwork for 
ship ventilation, they cover at least partially the conditions 
maintaining in building practice. 

Other formulae on friction head given in trade publications 

^ "Gesundheits Ing.," Oct. 10 and 20, 1905. 
2 "Transactions N. A. and M.' E./' 1905. 
^ "Gesundheits Ing.," July 1, 1905. 



THEORY OF THE FLOW 103 

such as p= , (d in inches), are mostly simphfied varia- 

25000 d ' J f 

tions of those quoted. They include f in a constant which is vir- 
tually correct within certain limits. 

The results of the various formulae, when plotted on loga- 
rithmic paper, show a fairly close agreement of the lines of di- 
ameter and velocity, if charted only within the range from which 
they are derived and known to apply. The slopes of the diagram 
presented strike about the average and will be found to give safe 
values for the friction in fairly well made sheet metal ducts of all 
sizes and velocities that may occur in ventilating work. 

The slope of the lines on the logarithmic chart when expressed 
in figures, as was done for water and for steam will make the, 
pressure loss in pounds per square foot. 

v^-^ 1 
Pf = w. 5.13f — for round pipes 



V' 



1.18 



and Pf==w. f — ( — I 1 for ducts of any shape. 

In this formula w is the density, v, 1 and d are again the 

velocity, length and diameter of conduit in feet. The value f is 

a constant expressing the coefficient of friction in the equation 

v^ 1 ^ c 

hf = f -—when v= 1 ft. and d = l ft., or when ~ = 1 for square 

^ 2g d ' a ^ 

ducts. The charted average makes it .032 for round pipes, and 

.032 

-—^ = .00624 for ducts of any shape. This figure is slightly in 

excess of most of the experimental data on f available and apply 
ing to these conditions, also of the results of Weisbach's and 
Grashof's formulae for f. It is therefore shown to be conservative 
and applicable to reasonably well made conduits at any range 
of diameter and speed. 

Factors of Local Resistance. — While the coefficient of friction 
has been investigated liberally and is known for all sorts of con- 
ditions, so as to bring the loss of head from that source well within 
the limit of error, the factors of local obstruction for changes in 
shape or direction of conduits, which usually present the greater 
resistance in ventilating systems, have received comparatively 
little attention. For many features, even the most frequently 
occurring, the data published is still incomplete or indefinite. 



104 THE FLOW OF AIR 

These various forms of local resistance are not comparable to 
the standard types or patterns of pipe fittings. They should be 
designed to suit the requirements of the individual case, but per- 
haps more often they are shaped to suit the taste and habit of the 
individual designer. For junctions or breechings, where the re- 
lations of static and dynamic head will enter, the factors must 
necessarily be variable, and cannot be charted, but for other 
items the values of r can be approximated sufficiently to cover 
average conditions. 

As explained in the general chapter, the loss of head by re- 
sistance, which is generally taken to be a function of the veloc- 

ity head — , is assumed to vary as the friction head. Accord- 

ingiy, pj. = w.r — , making the lines of resistance parallel to the 

lines for area, and giving the pressure loss in pounds per square 

foot for any velocity within the range of the charts. 

v2 
In order to give the approximate relation of r to — which 

2g 

would be correct in the above formula only for v = l, when 

y2_yi.9^ the factor has been taken as a function of the velocity 

9.252 9.251-^ 
head at 9.25 ft. per second, for which wr = w 1.25r 

2g 2g 

v2 
the constant 1.25 being equal to -— -. For -that velocity, we 

yl.9 

can write therefore Pr = w 1.25r — . For other velocities this 

2g 

will not change the results of the formula as given first, but 
changes the value of r to allow a fair comparison with the coeffi- 
cients of resistance measured by the velocity head, or quoted 
elsewhere in standard publications. For higher speeds than 
9.25 ft., Pj. figures less, for lower speeds more than the factor 
r indicates. 

Simple Forms of Resistance. — The various shapes selected are 
those most frequently occurring in practice. The factors for 
bends of different radius represent the average of the coefficients 
as given by Weisbach, Rietschel, Recknagel and others with an 
allowance for imperfect construction. They may be applied also 
to rectangular cross-section, whether the turn is on edge or side- 
ways, as long as the proportion of radius and width or diameter 



THEORY OF THE FLOW 105 

in the plane of deflection is as stated, excepting for knees and 
bends in very flat ducts, for which the coefl&cient increases 
decidedly when the turn is on edge. In extreme cases the resist- 
ance becomes a very uncertain factor. Turns of more or less 
than 90 degrees may roughly be assumed proportional to the 
angle of deflection, although this is not strictly correct. If two 
bends or other shapes deflecting the current follow in close suc- 
cession, the factors for both may be materially affected, accord- 
ing to the distance between. An offset or S figures more than 
the turns composing it. For round pipe, elbows are made up 
in sections, about as shown. The imperfect curvature of these 
bends is expressed in the factors. Bends of larger radius, are 
negligible items. Dampers without projecting frames or edges 
need not be taken into account. 

The loss of head by discharge through an orifice in a thin 
plate, illustrated by No. 1 on Fig. 24 is given for a coefficient of 
efflux = .6. It is assumed that the pressure is lost partly as the 
dynamic head of discharge, accelerated by the contraction and 
partly as static head expended in overcoming the resistance of 
the orifice, the total being expressed again as a function of 



V 



1.9 



1 . 25 , based on the velocity corresponding to the outlet area. 



2g 



The contraction in such an orifice is known to vary with diameter 
and velocity. The above formula follows these variations at 




3 4-5 

Fig. 24. — Types of inlets and outlets. 

least partially. With the stated coefficient of efflux it should give 
safe values for average cases. This factor does not apply to the 
frictionless orifice with rounded throat, but only to sharp edged 
openings in a thin plate, involving considerable contraction of 
the stream beyond the area of the opening. 

Discharging air through a pipe involves a pressure corre- 
sponding practically to the velocity head at the points of exit, no 
matter if the outlet is straight, converging or enlarging, as long 
as no contraction or eddies occur. The actual variations of this 
factor for the three pipe ends, Nos. 2, 3 and 4 shown on Fig. 24, 
do not appear to have been established, but they would probably 
differ but little from the dynamic head of the discharge based on 



106 THE FLOW OF AIR 

the exit area, which is well known to affect delivery to an appre- 
ciable extent according to the mouth-piece selected. 

Of the three styles of inlets No. 5 and No. 6 present a decided 
resistance owing to contraction, which are given approximately 
on the chart for air blast. The factor is based again on the 
velocity corresponding to the actual area, not of the contracted 
stream. In No. 7, the ideal contractionless orifice, the two 
velocities are identical. For an inlet into a pipe, the resistance 
of this ideal throat is negligible. When used for an outlet from a 
plenum space, the loss of head is practically that due to the full 
theoretical velocity, or the entire pressure head, the orifice being 
the equivalent or blast area. 

Equivalent Area. — As stated in the general introduction, the 
equivalent area is that corresponding to the discharge velocity 
resulting from the total pressure available at any point of a 
conduit system. It is the area to which a duct may be contracted 
without affecting delivery, provided, the contraction and ex- 
pansion of the stream is gradual and does not involve losses of 
motion. Any sudden impact and eddies causes a loss of pressure 
which should be taken into account and subtracted from the 
total available. The charts will give the theoretical velocity 
at the intersection of the dotted line with that of the pressure 
available, and the equivalent area is found along the same 
velocity line, where it intersects w^ith the ordinate for the volume 
to be carried. 

If this analysis for blast area is made, it is often possible, 
quite contrary to popular notion, to contract the area of a duct 
by a considerable portion, without curtailing delivery. Throt- 
tling takes place only through a reduction beyond the blast area, 
or through forms of contraction that will create a loss of motion 
with consequent decrease of the pressure available and corre- 
sponding increase of that area. 

The ideal form of contraction with least resistance is simply 
formed on the lines of natural flow through a sharp edged in- 
sertion as shown on Fig. 25, or the lines, on which the ^'Ven- 
turi" meter is shaped, which is known to present but a very small 
resistance to the flow. The area at the waist in this case might 
be reduced to the theoretical equivalent, for which hy^ = H and 
H — hv^=0, the entire pressure available being converted in 
passing from a to b into velocity head, and reconverted from 
b to c into the original relation of static and dynamic head. 



THEORY OF THE FLOW 



107 




Lines of natural Flow through contraction 



H-tiv 



<^ 



K-tiy, 



H-hu 



Ideal contraction oF conduit with least resistance 



rp^ 




Shape of obstruction presenting least resistance 




Loss of motion in elbow avoided by Forming it on lines oFcontraction 
Fig. 25. — Shapes of contraction and enlargement. 



108 THE FLOW OF AIR 

Obstructions in conduits that would otherwise curtail delivery 
can be made to avoid pressure losses and assure a full volume 
when shaped on these lines. 

Gradual enlargements, when built as shown, likewise will 
obviate losses of motion through impact and counter currents. 

It is also possible to reduce the resistance of a sharp elbow in 
the manner indicated on Fig. 25 by forming it on the lines of the 
natural flow, involving a contracted area. Loss of motion can 
thus be avoided through prevention of eddies, and resistance 
eased thereby, even if no space is available for an open bend. 
It may not always pay to design ductwork on aero-dynamic 
lines, but in cases where power must be saved, or dead corners 
avoided for other reasons, the contraction and enlargement of 
conduits on this principle is indicated. 

As previously pointed out, the reduction should in no case go 
beyond the equivalent or blast area. This latter is easily 
determined when a duct system is calculated for pressure loss, 
the total available being known for any point along the line. It 
is well to bear in mind when reducing a conduit, that the theoret- 
ical area varies between the blower and the suction and dis- 
charge ends of the system, being smallest at the former and 
nearing the duct size toward the latter. A conduit may there- 
fore be contracted to a smaller area at the fan than near the 
discharge end, according to the actual pressure maintaining at 
that point and available for conversion into motion. 

Composite Forms of Resistance. — All values of r, as given, are 
necessarily approximate, since they vary in some cases with the 
direction of the flow as indicated on the charts, and are influenced 
more or less through other circumstances. No comprehensive 
rules exist to define these variations. They are appreciable, but 
generally within the limit of error from other sources and can 
therefore be neglected in ordinary practice. This applies 
principally to the composite factors for portions of apparatus, 
typical and frequently used, which are included for convenience. 

For registers, the factor is made up by the sum of losses in- 
cident to the changes in direction and velocity in passing from 
the flue into the room. It is based on the speed in the flue, and 
is practically the same in either direction. The factor is given 
for square flue ends used in forced ventilation to secure a straight 
outflow, and for ends rounded to ease the flow for gravity work. 
The resistance is not materially affected by shutters or dampers 



THEORY OF THE FLOW 



109 



when these are turned parallel with the direction of the flow, 
and it is safe to assume the same factor for registers with and 
without valves. This appHes also to registers on the end of a 
straight run of duct. Registers on the side of a duct usually 
require some means for throtthng off an excess of pressure, in 
the shape of a narrow throat, or a perforated diaphragm. The 
resistance of such devices must be made to suit the pressure 
available at that point of the main. They should be considered 



^"^o5o9o9s?' 



^ ^ O ^^^^' ""' 

a Hof blast ceil, staggered rows, with sectional headers 
Net area about 407o of gross area 



-cQr-Qy-Q O -Q 




b Return bend coll, straight rows, made up oF Fittings 
Net area about 50% oF gross area 

Fig. 26. — Resistance of hot blast coils. 

as branch pieces or orifices and figured on the principles developed 
for them in a separate paragraph. 

Heating or tempering coils and indirect stacks offer very con- 
siderable obstruction. They usually cause the greater part of 
the entire pressure loss in forced systems, especially where the 
velocity between pipes is taken high in order to secure a great 
heating effect within a small space. It is primarily the relation 



no THE FLOW OF AIR 

of the net area between pipes to the gross area or cross-section 
of the casing which determines the factor of resistance. The 
arrangement of pipe heating surface commonly used in connection 
with ventilating and hot blast work are illustrated by Fig. 26. 
Arrangement ^^a" represents a typical hot blast coil with 
the pipe rows staggered to increase their heating efficiency. 
The free area for this style of coil is generally about 40 per 
cent, of the gross area. If the changes in velocity were not 
eased by the rounding of the pipes, and the speed between 
the rows brought down to that for the gross area, the loss of 
head for each pipe traversed could be expressed by the formula 

r = 1 — I — ) in this case 1 — I — ) = .84. Owing to the close 

\ag/ \2.5/ 

spacing of the pipes the momentum of the flow is maintained 
from row to row, to an extent which can only be estimated 
roughly. Moreover, the losses of head by contraction are 
avoided and eddies are materially lessened by the rounding of 
the pipes. It is safe to assume that the factor is reduced thereby 
to at least one-half of the above value, r = . 42, to which is to 
be added an allowance for friction, figuring about .03 and 
making r= .45 for each row of pipes. In estimating the factor 
for the coil as a whole we are to add the extra loss of head after 
passing the last row and allow for obstruction due to headers 
and support. For a typical hot blast coil of n rows we may 
therefore compute r = .45 n + .G. The lines of resistance on 
the chart are based on this estimate and check as closely as can 
be expected with experimental data on hand. The recent tests 
at the experimental station of the Royal Technical Institute,^ 
Berlin, for instance, show the pressure losses to be about 20 
per cent, smaller, on the average, but for a different spacing of 
pipes and without fittings, braces and other incidental obstruc- 
tions. 

Type '^b" is a straight row coil generally made up with 
return bends, for indirect heating. The spacing with close 

a 
headers and open bends will give a ratio for — of about one-half, 

ag 

making the theoretical factor per row 1— (I =.75. In the 

1 " Mittheilungen der Priifungsanstalt fiir Heizungs und Liiftungseinrich- 
tungen," Heft 3. 



THEORY OF THE FLOW 111 

straight passages the speed of the air is likely to be maintained 
somewhat more in this coil than in a staggered one, but the loss 
of motion by eddies is probably greater. Considering these 
points we are safe in assuming again r = . 5 X • 75 + . 025 = . 4 
for each row, and r = . 4n + . 5 for the coil as a whole. 

It would be impracticable to calculate and give the resistances 
of the various types and makes of cast iron indirect heating sur- 
faces. Some of the best are no longer in the market and the 
ideal design, combining the least resistance with the greatest 
heating effect still remains to be developed. Each manufacturer 
should test not only the emission, but also the friction loss for 
his particular designs, under stated conditions, and should 
present this information in the catalogue or on application. 
Engineers may then themselves insert this data in the charts 
for the styles which they are in the habit of using. In the 
absence of such figures, it is best to estimate the factor of resist- 
ance by comparison with similar forms and items of obstruction. 

The resistance presented by the casing of a coil or stack bears 
little relation to that of the pipes or sections and should be 
considered separately, according to area and shape of inlet and 
outlet. The inlet, when equal to the gross area as would occur 
in connection with a chamber, presents slight resistance owing 
to the low velocity. Connecting with a duct, the velocity head 
maintaining in the same at the entrance is nearly all lost, unless 
the enlargement to the gross area of the coil is very gradual. It 
is safe to assume r=.8 to 1. An outlet converging under an 
angle of about 45° will offer the same obstruction as a cone-shaped 
mouthpiece for which r = .6. When built at right angles, with 
a round opening opposite the fan inlet r is to be taken = 1. The 
factors for stack casings can be estimated in a similar way on 
hand of the various forms given on the charts. If one or two 
sides of the duct are flush with the casing, the factors for entrance 
and exit may be correspondingly reduced. 

Air filters of cheese cloth naturally check the flow of air 
according to the free area of passage, which depends not only 
upon the actual surface and the quality of the cloth, but also upon 
the amount of deposits gathered on the same. The factor is 
therefore necessarily an uncertain quantity, but it is none the 
less important to make allowance for this item of resistance. 
The velocity of passage is generally based upon the filter area 
or cloth surface. The actual speed between the meshes, by which 



112 THE FLOW OF AIR 

the factor might be measured, is much greater. Assuming it to 
be lOv, and basing the factor on that speed, a fair estimate 
would be r=l for loss of speed plus .5 for deflection through 
oblique passage. For clogging to one-half clear area we may 
put r= (1 + .5) X 2^ = 6. This factor checks with figures 
obtained for filters in fair condition, and approximates the 
results from the formula given by Rietschel for cheese cloth. 
For cotton flannel the resistance is from 10 to 20 times greater 
at the same velocity. 

The losses of head at entrance and exit to the filter chamber 
should be calculated separately according to the respective 
areas and shapes. 

Air washers with baffle plates, also other forms of filters, 
may be figured approximately as a combination of given factors, 
or estimated roughly by the losses of headway that may be 
involved. 

Velocity Head. — The third item in the sum of losses making 

v^ 
up the total pressure is the velocity head P^^ w — . It is under- 
stood to represent the dynamic head maintained at any point 
along the conduit which must be the difference between the 
total P and the static head Pg, the unused part of the resistance 
head. The charts give its value in pounds per square foot by 
the special dotted line at the intersection of those of velocity. 
As an item in the calculation of the total pressure, P^ is to be 
added only when sudden reductions of speed occur through 
features outside of those for which the factors are charted. The 
head-way lost in the items given, for instance that for registers, 
is always included. 

Variations of velocity through changes of area, such as occur 
at junctions, generally involve a partial conversion of the 
dynamic into static head, or vice versa. Only the losses of 
motion caused by these reducing or enlarging branch pieces 
are to be added to the total. Under gradual changes in area, 
when conversion takes place the losses incidental to it are 
negligible, but for pieces built indifferently on straight lines 
with decided angles of defiection, the drop in dynamic head 
practically expresses the head to be added as a loss. 

According to Weisbach and Carnot-Borda, the resistance head 

w 
involved by sudden enlargements will figure \ = -— (v — vj^ 



THEORY OF THE FLOW 113 

Blaess^ calls attention to the fact that this formula does not 

apply strictly to elastic bodies. His tests would indicate that for 

w 
decided differences of speed, the loss is nearer to hj. = — {y'^ — y^^). 

2g 

In such cases it would seem to be safer to use the latter formula, 

giving the drop in dynamic head, except where this drop is a 

small fraction of the total, in which case only a part of the stream 

is dissolved into eddies and the former expression is more nearly 

correct. For Vi = 0, or Vi = v, the result would be the same 

from either formula. The values for both can be read from 

the chart by subtraction of the values for Py and Pyi, or sub- 

. . w 

traction v and v^, which gives the head — (v — vj^. 

o 

In ventilating practice it is good policy to design conduits to 
reduce these losses through reductions in speed so as to 
render them negligible. This can nearly always be done by a 
taper piece on easy angles. Increases of speed also involve 
losses of head, but only in so far as taper pieces may 
cause contraction and eddies. Losses of that character are 
also easily reduced or practically avoided by intelligent design, 
bearing in mind that the angles for contraction and enlargement 
of area should differ, same as the converging and diverging lines 
of the nozzle with least resistance. 

Generally speaking, it will pay to eliminate as much as possible 
the uncertain factors when laying out a conduit system. This 
may not be obvious at first, but the fact will force itself upon the 
engineer whose designs grow out of the calculation. 

Junctions. — Unless air is to be delivered against pressure, the 
head of the flow is usually a large part of the total at any point 
of a conduit. It is necessary to consider it in problems of 
distribution. 

Branch pieces, breechings, or any other modes of joining two 
conduits into one, do not present any resistance outside of the 
portions of bends or the tapers usually connected to them, if 
designed to conform to the natural direction of the flow as it 
would result from the static and dynamic pressures at that point. 
In practice, the theoretical shape to fit this flow can only be 
approached, and some obstruction is unavoidable, but it should 
be kept down by appropriate shaping of junctions. This is 

^ Victor Blaess, ''Die Stromung in Rohren." 
8 



114 THE FLOW OF AIR 

desirable in order to reduce the total resistance head, as well as 
to eliminate the uncertain effect on distribution by improper 
forms of breechings. A fair approximation can always be as- 
sured by taking account of the pressure conditions in main and 
branch which give the throat velocity obtainable, and define 
at the same time the resultant angle of flow. 

If P is the total pressure in the main at the junction, P^ the 
velocity head, or pressure in axial direction, P — Py, or Pg is the 
static head or radial pressure in excess of the atmospheric. 
Calling P^ the back pressure caused by resistances in the branch, 
the radial outflow would be governed by Pg — P^ or P-P^-P^j = 
Pvi- The diagonal of the parallelogram resulting from the 
velocities due to Py and Pyi gives the theoretical discharge 
velocity and its direction. Fig. 27 illustrates the aerodynamic 
conditions involved. 

When the two forces act at right angles, as is the case on a 
straight run of main, the sum of squares of the two velocities 
equals the square of the resultant or actual speed of discharge. 
Since the pressures vary also as the square of velocities, we have, 
accordingly, if y^ designates the actual speed in the branch, 

P, + P.,=Pv2, and V3==J^(Pv + Pvi)=J^(P-Pb) 

^ w ^ w 

It follows that the ratio ~ = sin. a, — = cos. a and™ = tang, a, a 
V2 V2 V 

being the angle under which the discharge takes place. Hence 

v, V 

we have V2 = — : = • Thus the natural direction of dis- 

sm.o: cos.« 

charge is given by the relation of velocity heads for main and 
branch. Either the angle a should be suited to this ratio, or 
the ratio may be suited to the angle by an increase or reduction 
of back pressure on the branch which controls the velocity in 
the same. 

If the branch, measured at right angles to the line of Vj 
gives a lower velocity than the theoretical, there will be a 
sudden reduction of speed, or loss of motion, which means loss 
of head. If the throat is smaller, the volume is necessarily re- 
duced, but only about as the square root of the area, since 
the back pressure is relieved as the flow is lessened. When the 
angle of the junction is chosen too large or too small there is a 
loss of head due to eddies and impact which is difficult to estimate. 



THEORY OF THE FLOW 



115 



In extreme cases it may use up all the head available, and even 
cause reverse action. Hence the importance of considering the 
form of breechings. 

Strictly speaking, the back-pressure P^ is purely that by fric- 




Velocify in Branch taken From a Straight t^ain 




Veloeify in Branch taken From a Curved Main 
Fig. 27. 



tion and obstruction. Whatever dynamic head is represented 
by the discharge itself, and by sudden reductions of speed are to 
be considered as making up the velocity head Pv2 resulting at 
the throat, which is being spent along the branch. In the 



116 THE FLOW OF AIR 

case of gradual enlargement of area with reconversion of motion 
into pressure, the gain of static pressure is to be subtracted from 
from Pb and added to it, when pressure is released into motion 
through a gradual contraction, or when extra head is needed 
to create higher speed of discharge than that maintaining at the 
branch piece. 

When the conditions defined above are met by design, the 
branch piece reaches its greatest capacity, or full efficiency, each 
shape and angle having its characteristic curve of discharge with 
the high point at a certain ratio of Pv and Pyj- This has been 
neatly demonstrated by Taylor's experiments for the U. S. N. 
previously referred to. At full capacity, for the ideal breeching, 
Pv represents purely the back pressure beyond the junction itself, 
Py and Pv2 the velocity heads at main and branch. Since there is 
no loss by eddies or otherwise, P=Ps+Pb+Pv2) oi" Pv + Pvi=Pv2- 

In order to get the full effect of v as a component of V2, a 
branch piece should be built to face the current. In other 
words, the connection should form the offset or reduction on the 
main, as indicated in Fig. 27. When the outlet is flush with the 
side of a conduit, even though the angle be taken correctly, there 
will be an increase of speed on the contracted side of the main 
opposite, with a deflection toward the side of the branch, but 
we cannot figure on the full dynamic head of the main. Only a 
portion of it, depending on the shape of the breeching as a whole, 
is utilized. It may be estimated roughly from the area facing 
the current. Losses of motion caused by incorrect branch 
pieces also affect the forward flow through the main. Wherever 
possible they should be made a negligible item by appropriate 
design of ducts. 

Abnormal conditions will prevail when the flow within the 
main is deflected by curves, as illustrated also by Fig. 27. The 
outflow is evidently governed by several factors. Branches on 
the outer side are favored by the direction as well as the strength 
of flow, the increase of actual velocity depending on the radius 
of curvature and the exact location of the junction. On the ^'lee" 
side, the reverse takes place. When the static head is low at that 
point, the eddies in the main may create a suction on the branch. 
It is difficult to compute the discharge under such conditions. 
Branches on curves should be avoided. It is best to join ahead 
of a turn in the main, not after a turn, since the flow is always 
disturbed beyond for a length of several diameters. 



THEORY OF THE FLOW 117 

The ratio of static and dynamic head may vary to a con- 
siderable extent, between the junctions of the same conduit. It 
differs also according to the method of distribution, that is, be- 
tween plenum and high speed. Since the shape of the branch 
pieces will not only affect the resistance, but also the effective 
area of the connection it is essential to select a form of junction 
that will at least be approximately correct. 

It will be clear from the foregoing argument, that form ^^a" 
in Fig. 28 is proper for an outlet from a plenum chamber under 
sufficient pressure to overcome the extra resistance due to the 
contracted current at the orifice. Outlet "b" avoids this loss 
by contraction and should be applied when highest velocity is 
to be obtained from a given pressure. For plenum chambers 
v=0, and a = 90 degrees. Hence it would be as disadvantageous 
to discharge under smaller angles as it is to use ^^a" and ^^b" 
on ducts with air in rapid motion. The wrong way is shown by 
the upper figures. 

The type of outlet illustrated by ^^c" is correctly applied 
when the pressure head in the main would result in greater 
velocity than is desirable, the branch being too short to create 
back-pressure by friction. In this case the extra head is ail 
converted into motion, the excess of which is lost in eddies after 
passing a perforated diaphragm. This form of throttling may be 
used also on mains with moderate velocity, but the effective area 
should then be measured across the natural angle of discharge. 
Diaphragms should not be used, however, where the static head is 
very low, or the velocity high. In such cases a short branch lead- 
ing off at a small angle offers better opportunity of equalization. 

Form ^^d" is for high-pressure and low velocity on the main, 
or for slight back-pressure on the branch. For a = 60 degree, 
Pvi=3Pv,Pv2 = 4Pv and V2 = 2v. This maintains, of course, only 
for perfectly shaped reducing and branch pieces. The forms ^' e" 
and "V^ are in order where Pvi=Pv, and Pvi = .33 Py, hence Pyg 
= 2 Py and Pv2 = 1.33 Py or a = 45 degrees and 30 degrees respec- 
tively, making v, = 1.41 v and 1.16 v. When the velocity in the 
main is high, or when it is desirable to keep it lower for the 
branch, still smaller angles are advisable, a = 22 1/2 degrees will 
makePyi = .17Py, Pv2== l.lTPy and V2= 1.08v. 

Near the end of a main, where little pressure head is left, the 
highest velocity obtainable for the last branches as a rule does not 
exceed materially that of the main. It follows that the angle of 



118 




THE FLOW OF AIR 



_J;^^ 



I , / 



Plenum 



ill 



-i-i 



Plenum -long branch Plenum -short branch 




High pressure -low velocity 
p,=P-P„--4P^,V2=2v,c(^60'' 



Pv^-P-P,-ZP^ 
V2^l.4lv,oc'45' 



Low pressure- high velocity 
Pv2=P-Pt> ='-3^Pv. Vf-l.l6Y.cc-30' 



JJ 





Long or crooked 
branch 



Short or straight branch 








A 1 

\ 1 

) ! 




1 


/ 





Branch at end oF conduit Odd branch piece, P^^^'IISP^; v^ 'I.Odvtheon 

Pv^=P-Pb = P-Ps 'Psf.Vz'V PvfPv&'^'z^'^ approximate actual 

Fig. 28. — Types of branch pieces. 



THEORY OF THE FLOW 119 

discharge must be as small as possible. The branch pieces take 
the form of breechings, as shown by ''g". The same form is 
proper when the resistance of a branch calls for lower velocity. 
In such cases the throat should be sized for the speed in the 
main. Any enlargements of area that may be necessary to equalize 
resistance beyond the breeching should be made gradual, so as to 
convert speed into pressure that may be available for overcoming 
resistances. In any event, it is important to proportion the 
throat areas to prevent contraction and eddies at the junction, 
with consequent uncertainty of distribution. 

Very frequently, branches are to be taken off on the straight 
side of a conduit, the reduction of size being on the top or bottom, 
or on the opposite side. In order to reduce the pressure loss in 
the taper piece, it should be built on easy slopes, with the branch 
starting also at a small angle w^herever possible, about as shown 
by form "h." If the branch creates a back-pressure suited to 
this angle, the loss by eddies will be shght, and the velocity 
obtained in the branch is practically that of the main. The 
combined area of a^ and a2 can be made about equal to a for any 
branches at less than 30 degrees. The area of branch pieces 
built in this style is clearly defined, while for branches starting 
with a throat as shown by the alternate to ^'h" the effective area 
is difficult to determine, especially when the branch offers little 
resistance, so that the natural outflow does not follow the lines 
of the throat. 

Type "h" with modifications is applied in>a great number of 
cases. Starting with small angles, say up to 22 1/2 degrees, it 
presupposes a back pressure on the branch nearly equal to the 
static head, and a theoretical branch velocity of not over 1.08v. 
The loss of head caused by the breeching itself reduces Py and 
Pvi by a fraction, hence also Pyg and the resultant y^- For a 
fairly well designed branch piece Pya therefore, closely approaches 
Py. If we assume Py = Py2 the loss entailed by the breeching 
will be sin.a^Py, which figures .15Py for an angle of 22 1/2 
degrees. The calculation of such a branch piece then reduces 
itself to the simple problem of making its back pressure, that is, 
its total resistance by friction and obstruction, equal to the 
static head, less the estimated loss in the breeching. Since the 
factors for outlets, registers and other items include also the 
incidental losses in dynamic head, it is best to add also all other 
losses of velocity head on the branch, thus making its total pres- 



120 THE FLOW OF AIR 

sure come up to P— .15 P^, or whatever fraction of P^ is esti- 
mated to be lost in branching off. 

If the pressure losses in the branch and junction are thus 
equalized to make up P, it is safe to assume that V2 approaches 
2v for sharp angles of 60 degrees, 1.41v for 45 degrees, 1.15v 
for 30 degrees, and will be about equal to v for branches 
starting in a forward direction. The throat velocity should 
never be less than the speed in the main, except for junc- 
tions on the inside of curves, or when poor shape of connections 
cannot be avoided. 

The back pressure, as a rule, can be regulated by the length 
for which the size of the throat is maintained, and by obstruc- 
tions. Thus it may be desirable to enlarge directly beyond the 
junction, or it may be necessary to keep an even size up to the 
outlet. If that does not offer sufficient resistance, the velocity 
as well as the angle of outflow from the main are to be increased. 

The losses of head in the breeching, for the main itself, are not 
material when branch pieces are designed to reduce deflection 
of current, and to avoid sudden changes in speed. In taper 
pieces built on easy angles they are negligible. Ill-fitting 
shapes with sharp angles, however, are decided obstructions. 
Deflectors in the form of ^'scoops" for certain branches will 
also seriously impede the flow and reduce the head available 
for outlets beyond. Such protruding scoops are make-shifts 
showing the lack of intelligent design. The correct shapes are 
developed by calculation. 

In general, it may be said that a system of air conduits for 
heating or ventilating purposes should be designed with a view 
to reducing all sudden changes of speed in order to eliminate the 
incidental losses of motion, which increase the uncertainties of 
distribution. The greatest continuity of motion with gradual 
changes in velocity is always more successful and often more 
economical. 

The same general principles as outlined for mains and branches 
under pressure, will also apply to conduits under suction, but 
it should always be borne in mind, that angles for enlargement 
of area, or reduction of speed should be smaller than those for 
contraction or increasing velocity. 

Total Pressure. — The auxiliary chart is to be used for the 
purpose of ready determination of the theoretical speeds, the 
blast area and the power needs. It gives a larger range of pres- 



THEORY OF THE FLOW 121 

sures, representing P, the sum of Pf, P^. and P^, for a conduit 
system, in pounds per square foot, which is the natural and most 
convenient measure for such calculations. For conversion into 
ounces per square inch and inches of water column, separate 
scales are given. 

For air blast at high velocities and for certain classes of venti- 
lating work the pressure P is always created by mechanical 
means. The blowing machines generally used for that purpose 
impart their power to the air in the form of motion and com- 
pression or static and dynamic head. Theoretically, propeller 
(axial) as well as centrifugal (radial) fans can be designed to 
yield pressure and velocity in almost any ratio and intensity, 
using the right proportions, curvature of blades, housing, and 
number of stages. The commercial types of single stage axial 
and radial fans cover a fairly wide range of conditions and will 
serve well enough in ventilating practice, when intelligently 
applied. Whatever economy might be secured by specially 
built machines would rarely pay for the additional investment. 

According to Murgue's theory the ideal centrifugal fan wheel 
with radial blades would produce a total pressure equal to twice 
the velocity head due to its peripheral speed. The resistances 
by friction, the losses of motion by impact in wheel and casing, 
also the short-circuiting by leakage around the rim bring the net 
pressure obtained by the ordinary type of blowers down to about 
one-half of the theoretical, making it simply equal to the head 
due to the peripheral speed. 

The velocity at which the air leaves the wheel is not identical 
with the tip speed, but is a component of tangential and angular 
speed. Blades curved backward will give relatively more static 
head at lower velocity of exit. They are indicated for blowers 
delivering against plenum, at moderate initial speed. When 
curved forward, the exit velocity will be greater than the tip 
speed of the blades, which is more advantageous for a free dis- 
charge or moderate back pressure. With the curvature of blades 
and proportions adapted to create about the right relation of 
dynamic and static head, the net pressure will be somewhere 
between the velocity head of the tip speed and the theoretical. 
The aim in selecting the right type of wheel should be again to 
secure the greatest practicable continuity of motion. To this 
end the unavoidable drop of velocity from the blade ends to 
the duct should be kept down by appropriate angle of exit, by 



122 THE FLOW OF AIR 

the size of outlet and the shape of housing. The latter should 
be designed to convert the excess of velocity into pressure with- 
out undue losses. It will not pay, however, to resort to extreme 
curvature of blades which would require stationary guide vanes 
and keep down the aerodynamic efficiency of the machine by 
increased friction. Small angles of exit also reduce the effective 
diameter of the wheel as measured across the outlets formed by 
the inclined blades. Where the speed of exit cannot be brought 
down to approach that of the discharge duct, a tapering outlet 
on the casing will reduce the dynamic head at a moderate loss. 
For the same reasons, fans without suction ducts should have 
large inlets, or funnel-shaped throats to secure a more gradual 
increase of speed. Two inlets will reduce the resistance of en- 
trance into the fan owing to the much smaller velocity, and 
thereby increase the delivery. 

When the commercial fan does not permit close adaptation to 
the static and dynamic heads desired, or when it is likely to give 
low efficiency for other reasons, the peripheral velocity should be 
assumed from 5 to 10 per cent, greater than that due to the to- 
tal pressure. On the other hand, when all the factors are known, 
and the blower can be selected intelligently, it is safe to take the 
tip speed from 5 to 10 per cent, smaller than the theoretical. 

The same principles will apply to other designs, such as the 
drum type and the pressure blowers, but the relations of tip 
speed and theoretical pressure will differ. As volume blowers 
the former give more dynamic head, and with blades curved for- 
ward the wheel may be smaller. The charted data as to speed 
and blast area is intended only for the ordinary type of cen- 
trifugal wheel. 

With propeller fans the static and dynamic pressure created 
will depend largely upon the slope of the screw, giving a greater 
or smaller relative motion. The velocity theoretically obtainable 
would be V = tang, a wherein a is the angle of inclination. With 45 
degrees at the circumference, this velocity, for a perfect screw 
operating without back-pressure, would be equal to its peripheral 
speed. In practical designs of such fans, only a series discs, im- 
perfect portions of the ideal helix, are used. Under the best con- 
ditions, with free inlet and discharge the theoretical velocity is 
only approached near the circumference, hence the low efficiency 
when operated against pressure. To create pressure, the angle 
of inclination should be reduced, giving less forward motion and 



THEORY OF THE FLOW 123 

more power to compress. The less effective portions of blades 
near the center can be cut off by cones at the inlet and outlet, 
guiding the air along easy lines, and with gradual increase of 
speed, toward the revolving discs. 

Fans of all types should be designed or selected strictly to suit 
the conditions of load, that is, to produce a certain pressure 
difference equal to the sum of resistances Pf+Pj., while giving 
approximately a desired velocity head P^ at the outlet and mak- 
ing up together the total pressure P. The fan capacities, under 
working conditions thus established, should not be estimated 
from those obtaining under free delivery or through the theoret- 
ical orifice as given sometimes in the makers' catalogues. Either 
mode of rating is liable to be deceptive, since the actual discharge 
depends both upon the pressures to be overcome outside and the 
efficiency wathin, or the closeness with which the requirements 
are met by the machine. The correct way to select fans would 
lead through a study of their characteristic curves under varying 
conditions of load. If such data is not available it is best to call 
for a fan that will maintain a differential pressure P, while dis- 
charging the volume at about the desired velocity, which velocity 
should approach that corresponding to the equivalent area at the 
outlet, as figured from the back-pressure on the fan. The 
manufacturer who knows the characteristics of his machines 
will then be in the position to select the most advantageous type 
and size. The manufacturer who does not know these charac- 
teristics, will be handicapped, either by competing with a 
machine that is too large, or by having to replace one that will 
not come up to a clearly specified performance. 

For heating and ventilating by gravity, the total pressure must 
be produced by differences of temperature or weight, the motion 
being produced by that portion of the pressure not consumed in 
friction and local resistances. The total pressure available is 
usually limited by various conditions. The charts give the ready 
means to determine pressure and velocities. A guide to their 
application will be found in a special chapter. 

Frequently, the head to be created by mechanical means is 
reduced or increased by differences of temperature. It is well 
to consider the effect when that disturbing factor is likely to 
bear on the delivery of a fan under normal conditions, since the 
heat may sensibly influence the pressure to be maintained 
and modify the design, the speed and the power requirements. 



124 THE FLOW OF AIR 

The charts for gravity work give the pressure to be added or 
deducted. 

Motive Power. — The theoretical power in foot-pounds to move 
a given volume of air against a certain resistance can be expressed 
as the product of the volume in cubic feet per second and the 

QP 

pressure m pounds per square foot. In h. p. it will be . 

This is the power that must be expended in overcoming the 
resistances Pf and Pj. outside of the inlet and outlet of the fan 
and in creating P^. The energy absorbed by the aerodynamic 
losses within the fan, also the friction of bearings, and of belts or 
gears, must be added in order to arrive at the actual power to be 
supplied by a motor. For a fan efficiency of 50 per cent., the 
motor should be designed to develop twice the power of blast. 
When lower efficiency is likely, it should be further increased. 

Granted, that the total pressure P has been determined ac- 
curately, with due consideration of all resistances, and corrected 
for lower barometric pressure, higher or lower temperatures, and 
any buoyancy or depression due to unbalanced air columns, and 
granted also, that the fan selected is doing its best work at the 
intended speed and pressure relations, the efficiency of the several 
commercial types will vary but little. A motor of twice the 
power should be ample under these conditions. For belts or 
chain gear, speeds below or beyond the point of highest efficiency, 
and other adverse factors, extra allowance should be made. 



CHART VIII 

AIR BLAST AT HIGH VELOCITIES 

THROUGH ROUND SHEET METAL CONDmTS 
At a Mean Temperature of 70° F. 



Pressure in lb. per sq.ft. 






Total pressure required P =p,+P,+P, (ml 


between fan inlet and outlet). 


Power to move Q against P in h.p. =^£ -! motive power (approximate). 


Tlieoretieal velocity to create P in ft. PS. = F=^2(,-|j (approximate tip 


speed of ordinary centrifugal wheel). 




Diameter of fan wheel in ft. D =~ (approximate). 


Revolution per minute " -^ (approxmiatc). 


Corrections 


For leakage add to the volume from .5% to 1.8% per 10 lin.ft. according 


to pressure, character of conduits and ratio of ~. 




to friction head. 


For air temperatures below or above 70° ¥., correct presure and horse 


power b). adcUng or subtradinB 17c for every five degrees of variation. 


For square, rectangular, or odd shapes of cross-section with equal area 


-ip, the friction head by (^)-". 




1 XI -1.1.5 




1X2 = 1.23 


Factors for square and rectangular shapes 


1x3 = 1.30 




1x4-1.50 




1X5 = 1.65 




/CO/l 





^ 
^ 


veiocny ,n 


tt.per sec- 


m 


1 


h^-.^ 


M 




-e — 


0, ^ 


- \ 


\^ 


ri^ 


m^ 


w 


1 




if 




-6 — 

-'i- 


~i 


sM 


^ 




i ' > n/i 


TvX 


VS" 


gMHyimr 




s . 




X 


SZ ^^ 


/%* ' ^ iJIbr 


ytnC 


s^ 


^s. \ 


/\> ;' 




C 






^^^^ 


'M^l^ffi 


/^^ 


^ 


^^¥ 


i:m 


h 

7 




S 


>$^^; 


III 


1 


1 




kirn 


a. « 


F 


-\ 


™ 
^\'"^^ 


mm 


^ 


1 


m 


Gm'M 


■i—'-_ 




/ \ 


/ 


^74-, 


Vr In. rS 


0\\^ 


/ 






t. 


1 


)\ 


rtM/iMmTmii 


2\x 


vN ' 


¥%)(//\M\K\m 


fl 


1 


y 


M^MJt 


iA rumi) 


s\y 


*s^ 




i^'-"4-V» 


J: 


/ 


1 


Ifzimnm 


vSv 


C)v 


ss^'^tm 


mi^^ 




y A 


' 1 


im 


X/.f'. 


sA.'i 


V 


x%W 


tM 


>''t 


^ 


u 


U 


7 /^ 




Si / 1 


N 


x«^ 


^^.'^^^ 



300 ICO 500 lOOOcu.f 



ir-yed in cu ft pe 



CHAPTER IX 
AIR BLAST AT HIGH VELOCITIES 

Chart VIII. — The chart for an- blast covers a range of conditions 
met in a great variety of apparatus, such as mine, tunnel and 
workshop ventilation, also blast and suction devices for indus- 
trial purposes. It is plotted for round sheet metal conduits usu- 
ally employed for such work up to any pressure differences handled 
by the commercial centrifugal blowers. The lines of velocity, 
diameter and pressure are based on the formula given in the 
general chapter on the flow of air as applied to round pipes. 
For square ducts the data will be found on Charts IX. and X, 
To follow general practice, the diameters are stated in inches, in 
place of the area. The friction head is charted for a length of 
10 ft. The factors for local resistance are those most frequently 
met in this class of work. 

Pressure and h. p. are calculated on the basis of w = .075 
which is the weight of air per cubic foot at 70° F., at average 
barometric pressure. For warmer or colder air to be kept in 
motion, without change in temperature and volume, as meas- 
ured in transit, the pressure and h. p. increase directly as the 
density and inversely as the absolute temperatures. The correc- 
tions to be made are stated. 

The variations in density due to the compression by fans and 
to changes in humidity, within the range of conditions likely 
to occur, are very slight and may be neglected in ventilating 
practice. 

The frequent corrections to the friction head, to be made for 
leakage and imperfect conduits, and the factors for square and 
rectangular cross-section, are also given. For odd shapes, with 

equal area, the friction head is to be multipHed by I -- 

but the increase of area to be made for flatness is only proportion- 
ate to the square root of the factor for the friction head. 

The auxiliary chart is arranged to determine the power require- 
ment, blast area, and tip speed of fans from the total pressure, 

125 



126 THE FLOW OF AIR 

as derived from the calculation. Separate scales are given for 
ready conversion of the pressure in pounds per square foot into 
ounces per square inch and inches of water column. 

Outline of the Problem. — The simplest proposition in air blast 
is to convey a stated volume through a conduit of given length. 
Sometimes the velocities of intake or discharge, or at other points 
are predetermined, or the power available for creating the flow 
may be limited. 

For a given length and pressure drop the volume varies ap- 
proximately as the square root of the fifth power of the diameter, 
and for a given diameter and head, it varies inversely as the 
square root of the length. To the nominal length should be 
added the equivalents in resistance of any obstructions on the 
run. It is most essential, therefore, to consider length and 
obstructions, and their relation to pressure and density. In other 

P H 

words, we should always take into account — - or — , the ratio of 

w.l 1 

height to length, or what may be called the slope of a conduit, as 

a 
well as the hydraulic (in this case aero-dynamic) radius — , or the 

c 

diameter for round piping. Calculations based on area and 

initial pressure alone are liable to be grossly inaccurate. 

For a simple conduit the problem then resolves itself into the 
calculation of the diameter and velocity when pressure and 
length are given, or into determining the pressure, if diameter 
and speed are fixed conditions. In either case the unknown 
factors can be obtained easily by chart. The equation is solved 
when all the items for Pf, P^. and P^, are counted up, and the sum P 
agrees with the pressure figured for the given or desired areas and 
velocities. 

The situation becomes more complex when stated volumes are 
to be delivered or collected through a system of conduits branch- 
ing off to several points. The total pressure to be maintained 
by the fan is usually made up of the suction at the inlet and the 
excess pressure available at the outlet. If the air is taken from 
and discharged against the atmosphere, the difference of pressure 
between the fan inlet and any intake, and between the fan outlet 
and any point of delivery, must necessarily be the same. In 
other words, the sum Pf + Pr + Pv7 when counted up from the fan 
forward or backward, will always equalize itself for any number 
of discharges, no matter what may be their size and distance from 



AIR BLAST AT HIGH VELOCITIES 127 

the impeller. Hence the branches must be proportioned so as 
to present an equal resistance while delivering the desired volume. 
In its elements, the problem is the same as for a single conduit, 
but multiplied by the necessity to figure and equalize resistances 
to several points for a common pressure head. It is further com- 
plicated occasionally by back-pressure or suction, affecting indi- 
vidual points of delivery or differences in buoyancy due to heat, 
which must be balanced. 

It may be questioned, whether it is practicable to equalize a 
complex system of conduits, if all the calculations are to be 
made by formula, but the method indicated in the following 
chapters with the aid of the charts should simplify the process 
and make it pay, mainly through greater assurance of results. 

Application of Chart VIII. — A scale plan in the rough of con- 
duits for air blast or suction may be used as a schedule on which 
the volume of air in cubic feet per second to be carried in such 
portions is to be marked. The preliminary sizes of mains are 
best determined on the basis of an even rate of resistance. 
Assuming first an initial velocity for the main, as experience may 
dictate, we can find the friction head per 10 lin. ft. at the inter- 
section of the corresponding velocity line with that of the di- 
ameter. If this gives a pressure loss of, say, .4 lb. per square foot, 
the reduced area of the main after each branch is found directly 
on the same horizontal line, that is, at the same rate per unit of 
length, for any number of cubic feet to be carried. In this way 
an entire system can be proportioned quickly with the velocity 
decreasing in a gradual and natural way. The sizes so obtained 
should be marked on the schedule, those for the connections and 
branches being of course only tentative and subject to correction 
as equalization will demand. For long duct systems, when the 
pressure must be kept up, the rate should be small, while in other 
cases, where space and first cost are limited, it may be necessary 
to work under more friction. 

The pressure losses for the entire system can now be computed 
from the chart on hand of this schedule. Beginning at the 
furthest or least favored point of discharge, the various items are 
added up for each individual run, that is, for the lengths within 
which the volume is constant. The sum of losses, when marked 
at each junction, will give the difference of pressure between it 
and the atmosphere, the total at the fan representing the pressure 



128 THE FLOW OF AIR 

against which the air is to be delivered. The intake, similarly 
figured, will give the amount of suction. 

The intermediate branches, nearer to the fan, shorter, or in 
favoring location, when proportioned by thumb rule, will invite 
the flow along the path of least resistance, that is, the short, 
straight branches offering less friction and obstruction will dis- 
charge more than intended. The greater tax on the main caused 
thereby increases the pressure loss toward the far end of the 
line and involves a reduction of discharge further away. Hence 
the necessity of equalizing the resistances through the branches. 
This can be done by modification of the sizes, shapes, length, and 
features of obstruction. One or two trials generally suffice to 
bring the resistance of a branch close enough to the pressure 
available. 

In equalizing the various branches it is important to take note 
of the static and dynamic head prevailing at each junction, in 
order to select the proper form of breeching or to estimate the 
resistance for a given type. Although the round piping does not 
lend itself as readily to the correct shaping of the junctions, in a 
general way, the branch and reducing pieces can be, and should 
be, adapted to the static and dynamic heads according to the 
simpler rules developed in the chapter on junctions. 

The figured schedule will finally give the total pressure differ- 
ence to be maintained by the fan. The size of blower and motor 
may then be determined, on hand of the auxiliary chart. At the 
intersection of the lines for the total volume, and the total pres- 
sure against which it is to be moved, we find the theoretical blast 
area and the blast power. The intersection of the line of total 
pressure with that of theoretical velocity will give the latter, 
which is approximately the tip speed necessary to create the 
required pressure with the ordinary type of blower. The size of 
wheel being defined by the blast area, this tip speed determines 
the revolutions per minute as per formula given on the chart. If 
the blast area of a standard size does not fit, the width of the 
fan should be changed. Large volumes to be moved against 
low resistancee thus will call for relatively wider wheels, and 
vice-versa. In cases where the width cannot be modified, the 
speed may be varied enough to obtained the desired volume, 
but at lower efficiency. 

Examples of Air Blast Arrangement. — Fig. 29, A and B, repre- 
sent two distinct tendencies in the design of blast piping. One 



AIR BLAST AT HIGH VELOCITIES 



129 



. 




Pr= 45 


lo' 

1 




Pr= .15 
'/3Pv=.32 




y 


15 f^M-K 


1 1 




-^ Pd=l.3Z 


r-f 








P = ZB4 


1 




P„= 97 


1 




PsH.87 


15' 




PbM.SZ 




P.r .35=.36R, 


1 




ct^SOjapprox) 


1 




Pv.,'Pv-l.3Z=Pv, 






15 Vrll8V 


1 II 


1 '' 




7,7^ 








Pf = .76 

, Pr = l,05 

/3Pv=l-36 

I , Pb=3.17 

{Bends n I'M Pd° 1.32 

9"/^ P=4.49 

. 2.05 

-i-'Sranches Ps=2.44 

Ui]iyi\ 10' long. P^*Pd-P,=3.l7*l.32-2.7 
=— ' fuming r;^ 

c<.= 30°approx,') 
I .VeM.ISV 



Total pressure '4.75 Ib.persqffr-.din.wafer 

column. 

Blast power- 2.6 h.p. Motive power --S.Zh.p 
Tfieo. velocity'63ft.-- Peripheral speed. 
Blastarea=nsq.rt Fan wheeh6''3 ' 
yeLtieadafoutlet=l.5lb.persqff.-.?8P 



L3 
*- 4Z"-, 



J t= 



A- Distribuiion at Low Speed 



>Scs/e 



Total pre5Sure=8.75lb.persq.Ft- 1.68 in. 

water column. 
Blast power-4.8t}.pl1ofivepower-9.6h.p. 
Ttieo. velocity =87 ft = Peripheral speed J J300 
Blast area -J.S^q ft Fan wheel- 5 ''Zh ' 
Vel head at outlet ^Z. 55 lbs. = 29 P 

B- Distribution at High Speed 



Fig. 29. — Examples of blast arrangement. 
Outlets on one side to discharge 18 cu. ft. at 2400 ft. velocity per min. 
Outlets on other side to discharge 15 cu. ft. at 2000 ft. velocity per min. 
Outlets on end to discharge 20 cu. ft. at 2400 ft. velocity per min. 



130 THE FLOW OF AIR 

is proportioned with the idea of saving in first cost through 
reduction of conduits and size of fan, while the other one is 
designed with a view to economy in operation. The proper 
method for any particular case is indicated by circumstances 
which may point one way or the other, but aside from the power 
question, the idea illustrated by example ''A'' will be found pre- 
ferable on account of the smaller motor, which partially offsets 
the greater cost for fan and conduits. It will also give greater 
assurance of good divStribution and smaller fluctuations under 
throttled delivery. 

As will be noted, the net performances are equal, the same 
volumes being delivered with the same velocity at outlets. The 
lengths of conduits and features of obstruction are identical. 
With the plan "A'^ the velocity is kept lower in the main, which 
approaches the function of a distributing drum or plenum cham- 
ber. Plan ^'B'^ on the other hand, is sized for higher speed, 
which involves also a proportionately greater dynamic head. 

Since a uniform diameter of main rapidly decreases the ratio of 
velocity and pressure heads, and a uniform velocity increases the 
resistance for the smaller sizes, the mains, in either case, are pro- 
portioned by the method outlined, for an even rate of pressure 
loss, which gives a gradual and natural decrease of speed. The 
ratio of dynamic and static head varies also from junction to 
junction, and for the same length of branches the angle of the 
breeching and its throat diameter ought to be graduated to 
conform. In order to simplify construction, the angle is assumed 
to be uniform for each set of branches, being made 45 degrees 
for the short ones with less resistance, and 30 degrees for the oppo- 
site row, presenting more back-pressure, and the resistances are 
varied to conform to the angle, by graduations of diameter. The 
initial speed v in the main for scheme ''A" is figured from the size 
of the first branch, the diameter of which is made to correspond 
to the prescribed discharge velocity Vj. For 45 degree angle, 

V = — = — —. This initial speed defines also the rate of 

cos 45° 1.41 ^ 

pressure loss, about .05 lb. per 10 lin. ft. The decreasing sizes 

for each sectional run are taken from the chart along the same 

horizontal line. For scheme ^'B" the last branch has been taken 

as a basis, the final velocity in the last section of the main figuring 

again about — ^— = — ^—. The rate of pressure loss in this case is 
cos a 1.41 



AIR BLAST AT HIGH VELOCITIES 131 

about 0.15 lb. per 10 lin. ft. for which the enth'e main is propor- 
tioned. 

From the foregoing assumptions all parts of the two systems 
can be calculated. The next step will be to determine the resist- 
ance in the first branch of scheme ^^A" and the last branch of 
''B," to which should be added the velocity head of discharge 
and the estimated loss in the breeching, the sum of these items 
giving the loss for the branch, or the total pressure at the junction. 
The pressure losses are then figured for each main, up to the last 
junction of ''A'' and the first junction of "B." These losses 
should include the friction as well as an allowance for lost motion 
in the reducing pieces. The net pressures resulting at the several 
junctions up to the other end of the main give the balances avail- 
able for all of the branches, and determines their size and design. 
The' variations of back pressure should correspond to the differ- 
ences between the junctions. If these differences are too great 
to be made up by the natural graduation of throat and branch 
sizes, it is necessary to resort either to throttling or to elongation 
of branches in order to make up extra resistance for equalization. 
The latter means is resorted to in the two examples. The 
branches are made long enough, not only to provide the means for 
varying back-pressure, but also to give sufficient length for taper 
pieces that would permit the changes of velocity without material 
losses of motion. 

The two schedules give the complete calculation for the 
extreme end branches. It is not necessary to go into the same 
detail for the intervening points of discharge when a system is 
uniform, as in the present example, as the characteristics and the 
sizes for the others are intermediate and can be found by in- 
terpolation. 

A closer analysis of the figures will show that the friction and 
resistance by elbows make up only a portion of the back-pressure, 
and are a small part of the total pressure at the junctions. The 
losses of velocity head, due to the necessarily imperfect form of 
round pipe breechings, are considerable. They have been esti- 
mated to vary from 2/3 down to 1/3 of P^, according to the taper 
on the main. The end branches facing the current are assumed to 
utilize more of the momentum of the flow in the main. The 
velocity head of discharge F^ is seen to be the largest item making 
up the total pressure. The pressure drop in the main includes, 
beside the friction at the stated uniform rate, a loss averaging 



132 THE FLOW OF AIR 

about one-third of the reduction of velocity head in each taper 
piece. Thus the drop in speed from a 25-in. pipe to a 22-in. pipe 
in scheme "B" for volumes of 124.5 and 89.5 cu. ft. will be from 
36.5 to 34 ft. per second, reducing the dynamic head from 1.55 
to 1.30 lb. per square foot, as per chart. This difference is not alto- 
gether lost, but is partially reconverted into pressure head, same 
as would be the case in an enlarging cone or nozzle. About 
one-third of this difference or .08 lb. should be added to the 
friction head for 15 ft. length which is .225 lb. to find the pres- 
sure drop along the main, between the two junctions. 

The static head Pg and the resultant Pyi have been figured in 
order to check Pyg, Vg the throat velocity and the angle. For 
one row of branches, at 45 degrees, it will be seen that Py is 
practically equal to Pvi; showing the angle to be true. For the 
smaller branches the uniform angle of 30 degrees is at least ap- 
proximately correct. An attempt at more accurate sizing, or 
variations of angle, would not pay in practice. 

The pressure losses for the balance of each system are made up 
of exactly the same items. The totals show a marked difference 
in favor of scheme ^' A," for which the pressure and blast power 
is less thian one-half. Conforming to the lower velocities through- 
out this system it is advisable to keep down also the tip speed of 
the fan. A wheel of the same diameter as used for B would have 
to be much wider, or run beyond its best speed to make up for the 
lack of blast area. A wider blower would also mean lower effici- 
ency, unless two inlets can be arranged. The peripheral speed is 
taken to be about the same as the theoretical velocity corre- 
sponding to the total pressure P. It is read from the auxiliary 
chart at the intersection of the line of total pressure, with the 
line for 1 sq. ft. blast area, any abscissa giving the corresponding 
speed in feet per second, which is the same figure as for the volume 
in cubic feet per second. 

The two examples are also instructive in the showing they 
would make under reduced head or throttled discharge, which 
can readily be estimated. A variation of volume carried in any 
part of main will make a decidedly greater difference from junc- 
tion to junction in the case of the small pipe, and affect the dis- 
tribution correspondingly. 



CHAPTER X 
FORCED VENTILATION 

Chart IX. — This chart is intended for the calculation of 
mechanical ventilating apparatus for buildings. The friction 
head is computed for square sheet metal conduits of a given 
cross-sectional area, stated in square inches, with the square feet 
in round numbers only, shown in dash lines. The losses of head 
are again figured for an air temperature of 70° F. It should be 
noted, that the friction head is charted for a length of 100 ft. of 
straight conduit, while that for air blast, where the straight runs 
figure relatively more, is expressed for a length of 10 ft. only. 
The coefficients for resistance by obstruction are given for the 
features peculiar to ventilating practice for buildings. The total 
pressure, power, blast area, and theoretical velocity are charted 
separately, in the same manner as for air blast. The corrections 
to the volume for leakage in transit, considering the lower pres- 
sures, are stated to be somewhat smaller. Other frequent cor- 
rections are given for deformed and poorly built sheet iron ducts, 
for masonry ducts, except glazed tiling, and for duct work of 
different shapes. Corrections to the total pressure for higher or 
lower temperature of the air to be moved are the same as for air 
blast. For variations of temperature within the conduit the 
data given on the chart for gravity hot air heating may be used. 

Outline of the Problem. — The carrying capacity of a given con- 
duit system for ventilation is calculated on the same principles as 
laid down in the previous chapter for air blast. The problems 
of distribution are similar, the air being discharged usually against 
atmospheric pressure. In most instances the velocities through 
conduits, and especially at outlets, are to be kept within certain 
limits for various practical considerations, and the total pressure 
required for moving the air is, to an extent, governed by these. 
The main problem consists in the equalization of the resistances 
for the desired volumes. This is accomplished by modifications 
of duct sizes at such points where the velocities can be varied and 
by the correct shaping of junctions and other features to con- 

133 



134 THE FLOW OF AIR 

form to the natural flow, thereby eliminating as far as possible 
the uncertain elements. The general rules will apply equally to 
pressure and to suction. 

Heat will sometimes enter as a factor in calculating the avail- 
able head. A study of such cases is presented in the chapter on 
gravity movements. The questions of power are generally sub- 
ordinate to other considerations, but it must be gone into in order 
to determine the requirements. Incidentally, it will lead to 
discovering such opportunities for economy, as will always 
exist. 

When all factors entering the problem are duly taken into 
account, the system equalized to a fair degree and the power 
established, the desired delivery is assured beforehand without 
the necessity of throttling excess volume at some points and 
shunting them to others. Subsequent adjustment of the distri- 
bution, especially in unfinished buildings, is vexatious and un- 
certain. Atmospheric influences constantly change during the 
process, and hardly ever affect all discharges alike. For these 
and other reasons it is difficult to effect really fair distribution 
by dampers and deflectors, and the result is too often a bluff. 
At best, it involves loss of time, waste of power and presup- 
poses a margin of safety or an excess of capacity nearly always 
representing extra expense of installation. Moreover, adjust- 
ments are most liable to be disturbed by incompetent hands, 
while a duct system without dampers is not easily tampered 
with, and not likely to be, if correctly designed. 

Computation on such lines involves a thorough study of the 
factors entering into play and induces intelligent design of con- 
duits, and of apparatus in general, with a view to meeting a 
given requirement most economically. Again, the application 
of scientific method results in such proportions and dimensions of 
conduit, as will minimize the effect on distribution of occasional 
and partial shutting of outlets. 

Atmospheric conditions will affect air distribution more directly 
than is the case with water or steam, in so far as the points of 
delivery are influenced by wind action and temperature. While 
such disturbing factors bear equally on well balanced and indif- 
ferently designed systems, the weaknesses of the latter are more 
liable to show and to be felt under adverse conditions. 

Application of Chart IX. — A system of conduits should be con- 
sidered as a unit, all parts interdepending. It should be pre- 



CHART IX 

FORCED VENTILATION 



Pressure in lb. per sq.ft. to create velocity p, = .075; 
" ■• " overcome friction p/ = . 075 

Total pressure required i*=p»+P/+Pr (net between fan inlet and outlet). 
Power to move Q against P in b.p. -^^=5 motive power (approximate). 

; (approximate tip 



%W 



Theoretical velocity to create P in ft. p.s. = K=-^ 

speed of ordinary centrifugal wheel). 

Blast area of fan or theoretical outlet area in sq.ft. A 

Diameter of fan wheel in ft. D = (approximate). 

60F , 
Revolution per minute n=yr— (approxmmte). 



For leakage add to the volume from 5% to 10% per 100 Unit, according Q 

to pressure, character of conduits, and ratio of — . 'J 

Tor deformed and poorly built sheet iron ducts, add from 10% to 30% ^ 

to friction head. t> 

For conduits built of masonry, except glazed tiling, add from 10% to to 

For mean air temperatures in conduits below or above 70° F., correct 
pressure and horse-power by adding or subtracting 1% for every five degrees ^ 

For round pipes of equal area multiply the friction head by (—J =.87. « 

r flat, rectangular, and odd shapes of cross-section with equal 
f the friction head by 

1X2=1.07 
1X3 = 1.18 
1X4 = 1.30 



'(M" 



FactoiB for rectangular shapes j 




FORCED VENTILATION 135 

sented by a schedule giving at a glance a general survey of the 
problem in distribution or delivery and providing a convenient 
vehicle for establishing the various factors, that is, the volumes 
to be carried at all points, the length of runs to scale, and such 
sizes as are predetermined by discharge velocities or other con- 
ditions. A schedule is useful also for the preliminary sizing of 
those parts of a system which may be varied for equalization. It 
is most easily made up from a rough tracing or print of the plan of 
conduits which will give the horizontal measurements. The 
vertical runs are of uniform length as a rule for each story and 
may be stated, together with offsets and other features, for each of 
the flues. Particulars in design or items of local resistance which 
do not appear on the plan, can be noted. The figures for the 
volumes to be carried are to be added up successively, giving the 
quantity for each part run between junctions with due allowance 
for leakage. These figures may be distinguished by colors or 
underscoring. The area of all portions with a given velocity can 
be read directly from the chart and the corresponding dimensions 
marked, according to the shape desired. 

The sizes of mains, as for air blast, if based on a moderate 
rate of friction loss will be found to require little revision in 
equalizing the system. Assuming an initial velocity near the 
fan outlet as experience may dictate, the chart gives at once the 
size required for the total volume. The proportionate area for 
the volumes carried in all other parts of the main is then found 
directly along the same horizontal line of pressure loss assumed, 
or established, by the initial velocity. Thus, for instance, a 
volume of 1000 cu. ft. per sec, moving through a square duct of 
34 sq. ft. area, at 30 ft. velocity, will cause a friction loss of .3 lb. 
per 100 ft. of length. One-tenth of this volume, 100 cu. ft., at 
the same rate of loss requires 5.8 sq. ft. area at a velocity of 
17.3 ft. per sec, and 10 cu. ft. require 1 sq. ft. area at 10 ft. 
velocity. According to the length of conduit, the power avail- 
able, and the space conditions, a higher or lower rate of friction 
loss may be maintained approximately for the entire length of 
mains. Ducts of decided flat rectangular shape should be sized 
with allowance for the increased friction head, as stated by the 
factors for correction. But it should be remembered that these 
factors apply to the pressure, while the area is to be corrected by 
the square root of the factor for friction head. Thus a duct 1X4 
should have only \/l.3 = 1.14 times the area of a square conduit 



136 THE FLOW OF AIR 

for an equal rate of friction loss. As a rule it is proper merely 
to round up the figures obtained for flat shapes. 

The schedule thus prepared now permits the calculation of 
the pressure losses for equalizing the resistance in connections 
and branches to individual outlets, and for determining the 
total pressure and power requirements. The procedure is 
the same as outlined for air blast; the successive losses being 
added up, starting at the far end of the line, or at the atmos- 
pheric pressure, and noting the increased pressure at each junc- 
tion up to the fan. The loss for a part run of uniform area made 
up of several items of friction and local resistance, is rapidly found 
along the same velocity line, and changes of dynamic head, as far 
as they involve losses, are found by simple subtraction of the 
velocity heads for the speeds in question, or parts of the differ- 
ence as may be estimated from the shape and angle of contrac- 
tion or enlargement. 

For equalizing the delivery through branches, the connections 
between main ducts and the flues are, as a rule, the parts on which 
the resistance can most conveniently be varied to suit the need. 
In some cases it will be found advisable to modify velocities in the 
flues, but this can be done only to a limited extent. When the 
losses of head for the outlets and flues at fixed speed are deter- 
mined, and the pressure maintaining at each junction is estab- 
lished, as stated, the problem of equalization is reduced to one or 
two tentative assumptions of the size and shape of these connec- 
tions, which will make up the same total loss for each point of 
delivery. In selecting the form of resistance to be introduced, 
it should be remembered that the requisite pressure drop can be 
effected in three ways, commonly distinguished as friction, 
obstruction, and deliberate loss of motion. The static and 
dynamic conditions in the main, also the friction and other causes 
of back-pressure on branches should decide the method to be 
adopted in each instance, as previously outlined in the chapter on 
junctions. 

Friction should be depended upon wherever practicable. This 
is done by keeping up the full velocity obtainable, or natural to 
the branch at the angle chosen, as far as necessary to use up 
the excess of pressure. To deter the flow by extra obstruction as, 
for instance, by using close elbows instead of bends, may answer 
well enough sometimes, but the method is not conducive to 
accurate work. Conversion of static into dynamic head, to be 



FORCED VENTILATION 137 

deliberately lost by discharge through an orifice, is necessary 
where branches are too short to cause a desired friction head. 
The velocity obtainable through diaphragms or orifices is readily 
found on the chart, if the back-pressure is known, but the extent 
to which the velocity head of discharge is lost by impact and 
eddies, or is reconverted into pressure by the throat, is difficult 
to estimate. Hence it is best to depend upon friction head to 
equalize resistances in uneven length of branches and for decreas- 
ing pressure at junctions. This simply means larger areas for 
greater length, or reduced area on short branches, for which the 
friction is easily and accurately calculated. It saves space and 
material, and results in lower velocities than those obtained by 
orifice, or half closed dampers, which are liable to cause noise. 

The right hand portion of the chart for forced ventilation gives 
the theoretical blast power and blast area for any volume, to be 
moved against any pressure. It contains also two separate 
scales for converting the pressure from pounds per square foot 
into inches of water column and ounces per square inch. The 
line for 1 sq. ft. blast area, at its intersections with the abscissae 
for pressure indicates also the theoretical velocity for a given 
total pressure, the figures in feet per second being identical as 
those for volume. 

The peripheral speed of the fan is thus practically read from 
this chart, subject to certain modifications. The blast or equiv- 
alent area corresponding to the total pressure determines the size 
of the fan wheel for a given type and proportion. For the ordi- 
nary six or eight blade paddle wheel the blast area A equals about 

DW . . . DW . 

, W being the width at circumference. is approximately 

true if W is the full width at inlet, or that of the housing, as given 
in the catalogues. 

As previously stated, the actual motive power will depend upon 
the efficiency of the fan, which depends again upon the nearness 
by which the commercial article will fit the case. The methodical 
use of the charts, by establishing the true requirements as to 
static and dynamic pressures, permits the selection of the type 
of wheel, with dimensions and angles of discharge that will at 
least approximately meet the theoretical lines drawn in the 
general chapter. The highest efficiency for a given machine will 
then coincide about with its working conditions and assure 
economical operation. 



138 



THE FLOW OF AIR 



louvred-j Inlet 
545qft gross 36sqft net. 




Rafeof friction loss in mam about .35 Ibs.persqft.per 100 lin.fi^ 
Total pressure required 4.65 Ib.persq.ft =.9 ins. wafer 
Horse power in blast 2.5 h.p. \ 

Motive power 5.5 h.p. ' '^ , 

Theoretical velocity 64npersec j@| ||„__^^„ 

Outlet velocity 32 Tt. per sec izz'l^g"" le" 

Blast area of fan 4.5 sq ft 1 1^"' ~]"' J_ ^ 

Wt^eel (blades-curved baxk) 6 ft '3 ft ' \~\ r.Z8"m6"' 

Peripheral speed 66 . jj) 

Revolutions per mm 210 |24'l 

Heights of flues-- lie"' 

15 ft to li* floor registers 

30- •2'^ ' ' I2'- 16 4^11; 16;; 

Gross areaof all regisfersequalsfWicefhefluearea. 
Net area equals 60% of gross area 
All flues have shdrp elbows ai base \^ 



Fig. 30. — Example of duct system for ventilating. 



FORCED VENTILATION 139 

Example of Forced Ventilation. — Fig. 30 represents a typical 
duct system for a ventilating apparatus. The scale plan of the 
ductwork is used as a schedule for calculation. The figures for 
the volume of air per second for each flue are underscored. The 
pressures are noted in circles. The rate of friction in this case 
has been assumed to average about .35 lb. per sq. ft. for 100 ft. 
length, including the correction for flat shape. This gives as 
much difference in pressure between the extreme ends as can be 
conveniently equalized by friction in the connections to flues. 
A lower rate of loss would require larger ducts, while a greater 
drop would involve a higher initial pressure, and make it 
more difficult to equalize, the first branches becoming still 
smaller. 

The sizes of the registers and flues being determined by various 
practical considerations, the pressure losses down to the base 
of each flue are figured definitely and marked. A branch of the 
full size of the flue at the extreme far end of the line gives the 
loss of pressure to the first junction. This loss includes a portion 
of the decrease in velocity head from the main to that branch, 
the former being sized to conform to the .35 lb. rule for the 
main. The taper piece at the breeching is designed to reduce 
this item to a small, almost negligible fraction. It will be seen 
that breechings for runs of uneven length taper unequally, 
but converge at equal velocity. Thus, the second or short branch 
is contracted beyond the junction in order to bring its resistance 
up to that of the first named long one. 

From the breeching at the far end, up to the fan outlet, the 
pressure losses between junctions are added up successively. 
They include slight allowances for the decrease in the velocity 
head opposite the branches or for the taper pieces on the main, 
where changes in speed take place. The branches are mostly 
taken from a flush side of the main. The sizes of connections 
from the junctions to the bases of the flues are chosen to offer a 
resistance equal- to the difference in pressure between the two 
points, including the probable loss due to imperfection of breech- 
ings. The velocities in these connections vary from that of the 
main to about 25 per cent, above it. The angles of branch 
pieces are increased correspondingly toward the fan, conforming 
to the higher speed of outflow necessary for equalization. The 
loss by eddies and impact is thereby reduced to a small fraction 
of P.. 



140 THE FLOW OF AIR 

The head produced by the supplementary heating coil is avail- 
able in winter only. Without the heated air column, the dis- 
charge would be appreciably reduced. A by-pass around the 
coil for use in summer is calculated to offer a resistance equal to 
the obstruction of the coil, less the buoyancy of the warm air in 
winter, which figures .2 lb. per sq. ft. for 50 degrees difference 
and 30 ft. height as obtained from the chart for gravity hot air 
heating. 

The main duct at the fan outlet is designed with an easy taper 
in order to save loss of motion in getting down to the initial 
velocity desired. To enlarge the fan outlet to the full size of the 
main would not avoid this loss, since the same reduction in speed 
would then simply take place inside of the housing, possibly 
under less favorable conditions and probably without being taken 
into account. It is better to reduce the outlet of the ordinary 
blower down to the equivalent area, if a gradual enlargement of 
the duct can be secured, such as will convert the excess of dynamic 
head into static pressure. For the present example we find 
the theoretical speed for 1.5 lb. pressure at the outlet to be 36 ft. 
per sec. and the equivalent area 8 sq. ft. The regular outlet 
would be 10.5 sq. ft. The actual area chosen is 9 sq. ft. The 
main duct is 12.6 sq. ft., but the reduction in speed is so gradual 
that practically no loss occurs from that cause. The drop of 
.18 lb. from the nearest junction is made up mainly of friction 
and the resistance of a slight bend. The pressure drop for the 
tempering coil and casing are stated as separate items, also that 
for the filter and the air intake. 

The total pressure required gives a tolerable speed for the fan, 
indicating blades- with a backward curve to bring the speed of 
exit from the wheel nearer to that of the outlet, which would 
reduce the losses of motion and tend toward higher efficiency. 
The peripheral speed is taken slightly in excess of the theoretical, 
to make up for the extra resistance presented by the single inlet. 
The latter also involves slightly higher motive power, which is 
based in this case on somewhat less than 50 per cent, efficiency. 
It is probable that this gives a safe margin of capacity, as the 
fan efficiency, under proper selection, is likely to be higher. It 
would be easy, in this case, if desired, to bring the motive power 
within 5 h. p. by reducing the resistance through the coils or in- 
take and make it safe to use that size of motor. 

Example of Coupling Fans. — Occasionally it is desirable to 



FORCED VENTILATION 141 

couple together a blower and an exhauster. Assuming the duct 
system for each to call for different volume and pressure, to be 
created by the same motor on the same shaft, the problem will 
be to find the proper relation in the diameter and width of fan 
wheels, so that each may work to best advantage. 

Taking for example an air supply system, to deliver 300 cu. ft. 
of air per second, against a pressure of 3/4 oz. or 6,75 lb. per sq. ft. 
The blast area is found to be near to 4 sq. ft. The theoretical 
velocity is 77 ft. per second. The diameter of a fan wheel with 
standard proportions, for which the width over all, W = 0.5D, 

DW 

and A = , will be ^=\/^Ai ^^ this case 5.66 ft. For the 

nearest commercial diameter, 5 1/2 ft., the width over all should 

4A 

be W = — = 2.9 1 ft. or, say, 3 ft. The speed for that diameter is 

60V ^ ^ 

==267 rev. p. m. 

Dtt ^ 

Coupled to the same shaft, the other fan must necessarily 

make the same number of revolutions, at which it is to deliver, 

for instance, 250 cu. ft. per sec. against a pressure of .55 oz. or 

5 lb. per sq. ft. According to the chart, this requires a blast area 

of 3.8 sq. ft. In order to create the desired pressure this wheel is 

to have a peripheral speed of 66 ft. per second. Its diameter is, 

therefore, predetermined, and will fi2;ure D= =4.7 ft. 

'^ ' ^ 267X3.14 

DW 4X3.8 

and for the same relation of , the width will be W = = 

4 4.7 

3.2 ft. The question now arises which is the proper commercial 
size to select. The next larger diameter will give more, and the 
nearest below an appreciably lower pressure than that needed. 
If the main ducts leading to this fan can be increased and 
divided for two inlets, and the resistance eased sufficiently there- 
by to bring the diameter area to the regular size of 4.5 ft., making 

4X4 
A = 4 sq. ft. and W= — ^ = 3.55 ft., then the next smaller diam- 
4.5 

eter will prove to be more advantageous, since both the first 

cost and operating expense are kept down. 



CHAPTER XI 
HOT AIR HEATING AND VENTILATING BY GRAVITY 

Chart X. — The movement of air created by difference in tem- 
perature, as utilized for warm air heating and ventilating by 
gravity, takes place at moderate velocities. The chart is accord- 
ingly made to cover a lower range than that selected for VIII. and 
IX. The losses of head by friction are again charted for lengths 
of 100 ft. for square sheet metal ducts. The area is given in 
square feet and fractions thereof, so that the three charts should 
supplement each other to an extent, one giving the diameter of 
round pipes, the other the area in square inches and the third the 
area in square feet. The features of obstruction are partly the 
same as those of the other charts, with some additional items 
referring mainly to gravity heating. 

The corrections for different kinds of conduits and for odd 
shapes are the same as those for forced ventilation. No allow- 
ances need be made for leakage, except when dealing with un- 
usual pressures or with very leaky ductwork. The corrections 
for temperature as affecting friction and head available are 
stated on the chart and further explained in the text. 

The auxiliary diagram gives the total pressure clue to differ- 
ences of temperature above 70° F. in heat flues, and below 70° F. 
between room or vent flue and the outside air, for any height, 
with the idea of determining the theoretical velocity, from which 
the actual flow can be estimated roughly and assumed as a basis 
for final calculation. The initial temperature of 70° F. covers 
the normal conditions. For abnormal room or vent flue 
temperature the factors for correction are stated. 

Aero-motive Force for Gravity Circulation. — The force creating 
what may be called a natural flow of air is the difference in 
weight between two connecting unbalanced air columns under 
the same atmospheric pressure. It can be expressed as the pro- 
duct of the mean excess of density of one side over the other, and 
the height for which this excess maintains. If w^ and W2 are the 

142 



CHART X 

HOT AIR HEATING AND VENTILATING BY GRAVITY 

THROUGH SQUARE SHEET METAL COXDUITS 



ractors of Res. 



-^Velocity of Heaf riue in ff per sec-->/ 

/ i iiiiii ii i i i iM i M.M i f I rr/ i 




HEATING AND VENTILATING BY GRAVITY 143 

respective weights per cubic foot and h the actual height in 
question, the resulting pressure will figure P=(Wi — W2)h. 

The height which would give the theoretical velocity of fall is 
not identical with h, but equal to the imaginary difference H 
which the two unbalanced air columns would show after reas- 
suming the same temperature. (See Fig. 31). 



We 



I ^^ 
_.t_ 



Fig. 31. — Effective head of heat flue. 



This differential height really represents the expansion of the 
heated column. It is the head H available for creating the flow. 
If the velocity and area are given, it is the head required and 
to be created by temperature difference or height. Rietschel 

expresses it by the formula H = (^— — ^ — -j— — —]h.. 



1 + atj 1 + at. 

In this expression t^ and t^ are the respective temperatures 
above the freezing point, and a the coefficient of expansion, also 



144 THE FLOW OF AIR 

at 32° F., at which the density w = .0807. The product wH 
must then equal the pressure P as defined above. 

If we substitute the room temperature, as the initial one, 
which is pretty uniformly at 70° F., the formula may be simplified 
to read 

H=h-^^h = fl-^\ 
Tf V Tf/ 

wherein T^. and Tf are the absolute temperatures in room and 
flue. The resulting pressure in this case is 

P = Wj.H = wJ 1-— Mh=(Wj.-Wf)h 

Inserting the value of T^. for 70° F., we have 

530' 



P = 0.075(l 

The pressures and theoretical velocities for heat flues are com- 
puted and charted on this basis. 

For vents we can write correspondingly 

T / T 

and P=Wo(l-^jh, 

which forms will give the effective height and pressure measured 
by an air column of outside temperature T^. Conforming to all 
other tables, in which the heights and resulting velocities are 
given for air at 70° F., we may also write 

p =Wf( -^— llh which must equal (w^ — Wf)h. 

As a rule, Tf is both the room and flue temperature and in that 

case P = . 075 (y -ijh 

The pressures created have been calculated by this formula, but 
the theoretical velocity is figured by the first one, giving the true 
effective height H which governs the fall. 

As indicated in Fig. 32, the height of the columns in question 
is not identical with that of the flue, but should be figured from 
the mean level of leakage into the room, at which level it is 
assumed that the air is being heated. This may not always be 



HEATING AND VENTILATING BY GRAVITY 145 

strictly true, but is probably the fairest average assumption 
where the inward leakage is not influenced by suction or pres- 
sure on the room, as Avill be explained in the chapter on 
neutral zones. 



lo 




Fig. 32. — Effective head of vent flue. 



The correction to the pressure for any room or vent flue tem- 
peratures above or below the normal 70° F., is figured simply by 



the ratio of P^. to P wherein 



10 



1- 



fc- 



146 THE FLOW OF AIR 

The factors are given on the chart for a range from 50° F. to 100° 
F. The corresponding effective height H^, and the resulting 
theoretical velocity V^ do not vary at the same ratio, but the 
error in the actual velocity is of no consequence for approximate 
sizing and does not bear on the final result at all, if the velocity 
obtainable is verified by the final calculation of pressure losses. 
For accurate calculation it is essential to correct the friction, 
resistance and velocity heads according to the temperature main- 
taining in the various parts of conduit. To facilitate this, factors 
are given for a liberal range, expressing the ratio for the increased 
losses due to greater velocity under expanded volume, and allow- 
ing for variation in density, according to the formula 

' \ 530 / 0.075 530 

If the pressure loss is read on the basis of the changed volume, 

the corrected pressure is 

Wf ^ 530 _ 

P = — — P = P 

"" 0.075 Tf 

The velocity head, or the pressure expended in motion is the 
balance left, or the net result after deducting from the total the 
losses by friction and local resistances 

P, = P-(Pf-Pr) 

Since Pf and Pj. depend upon the actual velocity v, which is the 
unknown quantity, the latter must be found by tentative assump- 
tion, until the equation between the velocity obtainable and that 
required is complied with, that is, until 

Q 

^, wherein Q= cu. ft. per sec. at 70° F. 
w a 

Tf Q 

If Q is corrected for flue temperature v=^ X — 

530 a 

Outline of the Problem. — Warm air heating by the indirect 
medium of hot water or steam is usually designed with individual 
heating stacks for each flue or room, connected with one or more 
air intakes, sometimes with filters and tempering coils. We have, 
therefore, the problem of equalizing the delivery to several flues 
with unequal resistance and unequal pressure available, same as 
is met in hot water heating by gravity, except that not only the 
levels are different, but usually also the temperature range. The 
situation is more complex also in regard to establishing the true 



^ w 



HEATING AND VENTILATING BY GRAVITY 147 

effective temperatures, or differences in density, and the heights 
that come into play. This feature requires study, particularly 
for open or interrupted circuits, subject to external influences, 
which are the rule rather than the exception. The greater ele- 
ment of uncertainty in the calculation of heat flues and vents 
lies in the assumption of these two factors. It seems necessary 
to define them more clearly. 



■@r. 



Mean 



mj 



70 r 

level of coo l ing 




12^16 



h-ZOFf. 
P--.I65 



12x16-- 



I35r 



Mean level \oF heating 



A 



5cu.rf.af70 T. 



30%free 



Scale m Feet. 

12 3 4 5 5 



Fig. 33. — Indirect heat with closed circuit. 



Mean Levels. — Any closed circuit within which air is alter- 
nately cooled off and heated again has two turning points where the 
fluid begins to rise and to fall. These points are naturally at the 
mean level at which heat is applied and given up. For hot water 
heating they are recognized to be the mean levels of boiler and 
radiators. For indirect warm air heating it is the stack and the 
heat transmitting surfaces of rooms, as illustrated by Fig. 33. 



148 THE FLOW OF AIR 

The vertical distance between them marks the height of draught 
h, which may be greater or smaller than the height of the flue 
proper. These mean levels do not necessarily fall together with 
the two points on a circuit where suction changes into pressure 
and vice versa, but will often fall apart, especially with unequal 
resistance in the up- and down-take flues and ducts. In a case 
like Fig. 33, the room would be put under a slight pressure if the 
heat flue is larger or shorter than the return flue, and under 
vacuum, if this condition be reversed. 

Neutral Zones. — Recknagel in his studies of aerostatics in 
rooms has termed the strata, at which atmospheric pressure is 
maintained ''neutral zones." On a closed, and tight circuit the 
points at which there would be neither excess of pressure nor 
suction, would be defined solely by the friction and resistance 
along the conduit. Such a condition, however, never exists in 
practice. Leakage at points where pressure or vacuum prevails 
will often depress or raise the neutral zones very considerably. 
On open or interrupted circuits, as for instance heating arrange- 
ments with intakes and vents to and from the atmosphere, ex- 
ternal wind pressure is liable to change the zone. Also the effect 
of one flue over another may radically disturb the static pres- 
sures along the line, even to the point of reversing the flow. 

While the shifting of the neutral strata will have no bearing on 
the volume of air in transit on a closed circuit, since one side can 
make up for the other, the raising or lowering of the zones on an 
open system virtually has the effect of increasing or decreasing 
the height of draught by adding to, or taking from the head avail- 
able for the movement in a flue. A too large heat flue, for in- 
stance, will depress the neutral zone in the room and decrease the 
height of draught necessary to create a given movement of air by 
creating an excess of pressure. The effective height of the vent 
is thereby correspondingly increased and its size may be smaller. 
The same effect may be due to wind pressure on the air intake, or 
suction on the vent. 

The influence of leakage on the neutral zones or the height of 
draught can be estimated with a fair degree of assurance and 
should be taken into consideration, not only in its possible bearing 
on the volume of air or the amount of heat required, but as affect- 
ing the static pressure in the room, and thereby the ingress and 
egress through heat and vent flues. A roojQ, or building as a 
whole, kept at higher temperature than the atmosphere, but 



HEATING AND VENTILATING BY GRAVITY 149 

communicating with it by leakage, will form an unbalanced col- 
umn of lighter air tending to escape on the top and drawing in 
heavier air at the bottom. As illustrated by Fig. 34 this tend- 




FiG. 34. — Indirect heat and vent open to atmosphere. 



ency for ingress and egress increases with the vertical distance 
from the neutral zone, that is, with the height of a room, or build- 
ing. It also increases with the difference in temperature between 



150 THE FLOW OF AIR 

the inner and outer air. Tall rooms may show considerable 
pressure and outward leakage in the upper strata, and show a 
strong tendency to indraught through doors and windows at a 
lower level. If this latter tendency is to be avoided, the air 
supply flue must be ample enough to reduce its height of draught 
or bring down its upper strata to a level below the points of inward 
leakage. In other words, the neutral zone is to be lowered below 
the level of windows and doors, and the system calculated and 
proportioned on the basis of these heights. The extra pressure 
to be exerted is easily figured as the product (w^— Wr)h or read 
from the chart, h being the height for which the zone is to be 
depressed. This applies to forced ventilation as well, if a room 
is to be put under fan pressure in order to avoid in-draughts. 

In a similar way, the neutral zone may be lowered by back- 
pressure, caused, for instance, by insufficient vent capacity. 
Such restriction of the volume at once reduces the effective 
height of draught for the heat flue. When the room is air-tight 
and the vent closed, the movement of air in the heat flue ceases 
because the height of draught is reduced to nothing. The 
upper and lower neutral zones fall together. While this condi- 
tion maintains there may be still some heat delivery through up 
and down circulation within the same flue, but the least addi- 
tional pressure on the room through inward leakage will reverse 
the flow. 

To what extent a moderate change in pressure, or a shifting of 
the neutral zone will bear on conduit area, is illustrated on 
Fig. 33. A difference of 5 ft. is seen to modify the flue sizes, 
especially that from an indirect stack, for which the margin of 
pressure to create the motion is materially affected. 

The height of a flue itself, as already mentioned, and the differ- 
ence in level between heating and cooling surfaces are, therefore, 
by no means identical with the effective height of draught, but, 
as may appear through further consideration, it is generally 
desirable to make them so. That is, the neutral zone should be 
laid at the mean level of cooling, which, at least theoretically, 
is also the proper level for a warm air discharge. 

Correct Height of Draught. — It will be realized that in practice 
various conditions will modify the height of draught to be taken as 
a basis for calculation. Living rooms on the lower stories of 
residences, when open to a stair hall, will show an increased 
height of draught, which may be estimated from the number of 



HEATING AND VENTILATING BY GRAVITY 151 

stories so connected. The mean level of exposure may also affect 
the height to an extent. Allowance should be made for wind 
pressure, unless its effect is neutralized by the situation of the air 
inlet. Rooms with only one side exposed are more liable to be 
under back-pressure through wind action when the warm air is 
most needed. If sufficient vent capacity is not provided, it 
may happen, and it does happen sometimes, that the room air 
escapes down through the heat flue, carrying the upper neutral 
zone even below the level of the stack. 

The investigation into the true height of draught should lead 
not only to greater assurance in the calculation of the expected 
flow, but should also lead to the modification of the height of 
the zone, placing it approximately at the most advantageous 
level through the proper disposition of air inlets, vent outlets, the 
closing of stair wells or providing an escape in the form of a fire- 
place or vent flue. Other means will suggest themselves tending 
to keep the movement of the air under control, as the case may 
require. It is advisable, for example, in fact often necessary, to 
expose the air inlet to the same winds as the rooms which they 
supply. Owing to inward leakage under pressure from the out- 
side the heat requirement is greatly increased. Simultaneously 
the neutral zone is depressed, and the supply of hot air is curtailed, 
unless advantage is taken of this same wind pressure to over- 
balance the inward leakage of cold air, by directing it also upon 
the air intake to the heating stacks. If so arranged, it is proper 
to figure on the wind pressure for overcoming a portion of the 
resistance. This may include that presented by inlet screens, air 
filters and tempering coils, but should not exceed the proportion- 
ate allowance made to the hot air supply for the exposure of the 
room, as will be explained by the example for warm air heating. 

The height of draught for natural vents is defined, like that for 
heat flues, by the vertical distance between the mean levels at 
which the air is heated and cooled, but modified again by external 
influences. The lower strata of balanced pressure usually lies 
within the room where the heat is applied or present in the warmed 
air contents, but it may be above or below its mean level, if 
put under pressure or vacuum. The upper strata is clearly at 
the outlet of the flue into the atmosphere. The same external 
or internal influences that may raise or depress the neutral zone, 
and increase or decrease the height of draught for the heat flue 
will also affect the height of the vent, but inversely. A heat flue 



152 THE FLOW OF AIR 

of greater capacity than the vent will put a room under pressure, 
depress the neutral zone, encourage outward leakage, making 
the vent more effective by reason of greater height of draught. 
Wind pressure on the room will have a similar effect. On the 
other hand, suction through communicating air shafts or stair- 
ways will oppose the upward movement in the flue by reason of a 
raised neutral zone and decreased active height. 

The heights of draught for heat and vent flues of the same 
room are therefore interdependent or complementary when ex- 
ternal influences are eliminated, but this is hardly ever true in 
practice. For that reason it is best not to consider them a single 
circuit, but to calculate each by itself, on the basis of the proper 
height. Due consideration of this height in question will lead to 
the discovery of disturbing influences, which may then be elim- 
inated or counteracted intelligently, as the case may demand. 
The bearing of this on the results is self evident. 

Among the disturbing external influences on vent capacity it 
is important to consider the action of winds upon the discharge 
opening. When located on the roof, these outlets are exposed to 
dynamic forces from all directions, tending to assist or upset the 
flow. These forces should be neutralized or regulated as much as 
possible by some form of top which will deflect the outer currents 
in the direction of discharge. Each case ought to be studied 
individually, and the right form selected on its merits. It is not 
proper to depend on these devices for creating suction, since that 
effect is available only under wind action, that is, when extra 
movement is least needed. It should also be remembered that 
vent caps in any form giving free exit, while stopping back- 
draughts from above, cannot prevent reverse action caused 
by suction from below, due to some disturbance of the neutral 
zone within. Such disturbances, aside from spontaneous effects 
through opening of doors or windows, are frequently due to 
peculiarities in construction which might have been avoided, 
or through the action of other flues when based on erroneous 
assumption of height and temperature. 

Temperature as a Factor. — The difference in the mean densities 
of the rising and falling air columns representing the second factor 
in the product of height and weight h (Wj.— Wf), is determined 
roughly by the temperatures of the room to be warmed and of 
the hot air flues, or by the temperatures of the flue and of the 
atmosphere for vents. The true differential weights, which 



HEATING AND VENTILATING BY GRAVITY 153 

create the power do not always correspond to these temperatures 
and are subject to modification. 

The temperature of the room air is presumed to be known, and 
can be taken as a basis for the density w^ of the colder column 
balancing that in the heat flue, but the temperature in the latter 
is liable to change in transit. When flues are placed in inside 
walls and are lined, the drop is a negligible item. Flues built 
into outside walls should either be insulated against heat loss or 
allowance should be made in the heating surface to make up for 
the same by higher initial flue temperature. For a given degree 
at the register this will raise the mean temperature, but, as a rule, 
it will not pay to take this into account. 

In the case of ordinary natural vents discharging into the 
atmosphere, the room temperature may vary considerably from 
the average maintaining within the flue, and the draught is thereby 
materially affected. In tall rooms for instance, under certain 
conditions, the temperature near the ceiling is liable to be several 
degress higher than near the floor. If a top register is used, the 
calculation of the vent capacity should be based on a higher 
temperature. This is all the more necessary as the friction head 
is decreased by a shorter flue, and, although this tends to raise 
the neutral zone, the decreased height is not likely to make up for 
increased heat. The temperature of a vent may also be affected 
by cooling or heating in transit, according to surroundings. Such 
temperature changes can only be estimated roughly, but it is 
nevertheless important to consider them, if only to avoid ex- 
tremes and uncertainties in general, by appropriate location 
or by special measures. Any heat supplied or lost in the vent 
should be estimated and the mean temperatures corrected 
accordingly. 

When the air supply to a room is determined solely by its 
heating requirements, the vent can be calculated for full capacity 
at the lowest outside temperature. It will then draw less air in 
warmer weather and regulate the amount of air supplied to an 
extent, approximately according to need. If a definite volume 
of air is to be introduced for ventilating purposes, irrespective of 
heating, its temperature must vary, and with it the pressure of 
inflow. The vent is then calculated to move an equal volume up 
to a stated outside temperature that may be varied according to 
the nature of the case. Provision should be made to control the 
action of such vents in colder weather. It is generally impracti- 



154 THE FLOW OF AIR 

cable to base the capacity of vents on outside temperatures above 
the freezing-point, since it will result in excessive flue sizes and 
lead to difliculties in regulation. If such vents are to have full 
capacity up to oustide temperatures that will permit the opening 
of windows in a crowded room, or if the flue space is limited, the 
increased draught power must be secured by heating the vent up 
to the required differential temperature, or by mechanical means, 
when indicated. 

Distribution. — The problem of distributing hot air, or of collect- 
ing vents is essentially the same as outlined for forced ventilation, 
but complicated somewhat, as stated, by the differentiation of the 
total pressure for the various points of delivery. When the heat 
source is central, only the heights will vary, except so far as the 
effective head may be reduced by heat lost in transit, as in the 
case of hot water heating, or ordinary furnace work. With an 
individual heat source for each room the density will also vary, 
and it becomes necessary to figure the pressures available in each 
case, as a basis for distribution. A system of ducts should be 
proportioned accordingly to balance resistances against the 
pressure created in each flue by its own heat. 

The effect on distribution of throttling one or more outlets is 
less disturbing on the delivery of heat flues in so far as each pro- 
vides its own motive power. If a main duct is designed for full 
capacity, the volumes passing through the flues left open is but 
slightly increased as the friction in the common passages is les- 
sened, that part of the resistance being small compared with 
the balance, represented by the individual stacks, flues, and 
registers. 

While there is a tendency to self-regulation in a warm air 
heating system owing to the probable increase of flue temperature 
at reduced velocity, this tendency is by no means as pronounced 
and dependable as in the case of hot water circulation, since the 
heat supply is not directly controlled by the air circulation, and 
other factors will enter into play. 

Under reduced head, that is, with lower flue temperature, ow- 
ing to a decreased output of the heat sources, the distribution is 
influenced mainly by the heat delivery to the stacks, which is 
presumed to be equalized. Since a shortage in heat emission 
means also a reduction of draught power, volume, and efl&ciency 
of heating surface, all interdependent, the effect is difficult to 
estimate. It becomes noticeable for instance where direct hot 



HEATING AND VENTILATING BY GRAVITY 155 

water heating surfaces on upper stories are allowed to get the 
best of the circulation to the stacks. 

Some of the conditions described as controlling the action of 
gravity heating and ventilating apparatus may appear at first 
glance to be too elusive to permit a safe estimate of the factors 
for reasonably close computation. However, the study of these 
conditions in itself gives the means to gain control over them to a 
greater extent, or to recognize and meet them as the case may be. 
The forces for creating natural movement are as positive as any 
that may be created by mechanical means, but limited as to 
potential. If the resistances can be suited to the pressure that 
may be available, a reasonably accurate prediction of the re- 
sult is assured. The charts make such calculation feasible and 
practicable. 

Application of Chart X. — The method of using the chart for 
gravity apparatus differs from that used in mechanical ventilating 
principally in the reversal of the proceeding as to establishing the 
working pressure. The pressure created, or available, is in this 
case the governing condition to be established first. When the 
principal factors, height of draught and temperature, have been 
sized up the resulting pressure and theoretical velocity can be 
read directly from the chart. They are subject to correction 
only when rooms to be heated or ventilated are to be kept at 
considerably higher or lower temperature than the customary 
70° F. 

For purposes of estimating, the table of pressures created gives 
the approximate actual velocity for various conditions. Indirect 
heating apparatus presents considerable resistance to the flow of 
air. Ordinarily, the actual velocity will not be more than 40 
per cent, of the theoretical. With air filters and tempering coils, 
it is likely to be even less. In vent flues discharging directly to 
the atmosphere without main ducts, the actual velocity is gen- 
erally 50 per cent, of the theoretical, sometimes more. 

These approximations should be used as a preliminary assump- 
tion for calculating the friction, resistance and the velocity head. 
The sum of these must always equal the pressure available, and 
should be made to equal it for the requisite volume of air. 

The volume is supposed to be measured at a temperature of 
70° F. It will be smaller when entering the system as cold air, 
and larger as a heat carrier between the stack and the room. 
The resistance is thereby appreciably modified, and the sums of 



156 THE FLOW OF AIR 

pressure losses for runs of uniform temperature should be cor- 
rected by the factors given for this purpose. In most instances, 
however, the decreased volume and pressure loss for the cold air 
ducts are about offset by the increased loss in the heat flue, so 
that the final result without corrections, is likely to come within 
the limit of error from other causes. It is only in odd and 
extreme cases that it will pay to take these factors into account. 

Individual heating or vent flues, each with separate air intake 
or outlet, may be figured without schedule. For apparatus with 
a duct system to be equalized for accurate distribution, the same 
mode of procedure is indicated as suggested for forced ventilating 
problems. The schedule of runs should, in addition, give the 
temperatures in each part of the system. Only the flues, as 
creating their own pressure, may be sized tentatively on the 
basis of the probable actual velocity resulting, which may differ 
radically according to the head available. The main ducts 
connecting them, on the other hand, should be proportioned for 
an even rate of pressure loss, as for blast work, and assuming as 
a basis the rate of loss maintaining in the connection at the far 
end of the line which should be the full size of the flue. 

The pressure available for each heat flue should be used up on 
the individual runs, if possible by the stacks and vertical flues 
beyond, so that the system of main ducts can be figured as being 
under definite initial pressure. If the throats or branch pieces 
do not give sufficient opportunity to equalize the flow to the 
branches, the horizontal connections to the stacks may be varied 
in size. The air will then be delivered at each stack casing under 
the same pressure, thus placing the lower neutral zone where it 
belongs — at the mean level of heating. 

Example of a Gravity Vent. — The ventilating arrangement 
illustrated by Fig. 35 is intended for exhausting toilets, locker 
rooms, etc., connected by an open stairway with a large gymna- 
sium above. The building is exposed on all sides. The ap- 
paratus shown is intended only for the heating season, when 
open windows are objected to. 

Individual vent flues from the several rooms of the lower story, 
the only one to be ventilated, were found to provide insufl&cient 
head since the neutral zone, under liberal leakage, and with the up- 
per hall connecting by two stairways, is likely to be at the mean 
level of exposure. The large area of roofing and skylight place 
this level above the gallery floor. For individual flues from 



HEATING AND VENTILATING BY GRAVITY 157 







158 THE FLOW OF AIR 

rooms located in the outside walls, and extending little beyond 
the main cornice, the effective head would be measured from 
the neutral zone to the outlets above the cornice. This small 
margin of effective height would be further reduced by cooling, 
which, at certain times, might offset it entirely and cause reversed 
action. A common shaft, which could be extended to a higher 
level promised better, but it became necessary to provide some 
extra draught power to overcome the resistance in the connecting 
ductwork. The smoke flue from the boiler was accordingly 
placed into this shaft, assuring an excess of temperature at least 
during the season when windows would be closed. 

Without the heat of the boiler flue the draught power would 
be given by the temperature difference between the rooms and 
the outer air, in this case 35° F., and the height of the shaft from 
the neutral zone up to the outlet, 30 ft. above. The auxiliary 
chart gives .16 lb. per sq. ft. The additional buoyancy created 
by the boiler flue may be figured from the total temperature rise 
in the shaft, which is estimated to be 24° F. and the height of the 
shaft above the mean level at which the heat is applied, which is 
somewhat below the middle, or about 32 ft. The chart for heat 
flues, to be used in this case, gives .105 lb. additional pressure. 
The same result will be found by taking the entire height of shaft, 
59 ft. and the mean temperature difference, which is slightly 
higher than half the total rise, corresponding to the greater heat 
emission in the lower half of the shaft. The total pressure avail- 
able is therefore, .16 + . 105 =.265 lb. per sq. ft., which must 
equal the sum of resistances in the ducts and the shaft, and give 
an approximate actual velocity of 7.5 ft. per sec. Allowing for 
resistance in the horizontal ducts and roughness of the brick flue 
the average speed was assumed to be somewhat smaller and the 
main duct and branches were proportioned for a rate of pressure 
loss of .04 lb. per sq. ft., per 100 ft., including corrections. 

The calculation of the pressure losses, as shown on the schedule 
bore out these tentative assumptions very closely, the areas being 
corrected only for equalizing the suction. Allowances were 
made for higher temperature in the shaft, also for the increased 

ratio of — , the greater friction of brickwork and for shallow 
a 

ducts. 

Example of Indirect Heating System. — The schedule of such an 

apparatus represented by Fig. 36 gives as data for calculation, the 



HEATING AND VENTILATING BY GRAVITY 159 




f leva f ion of Intake and Coil 



160 THE FLOW OF AIR 

volumes of air desired, the flue temperatures and the heights of 
draught for a group of indirect heating stacks connected to a 
common air intake. The windows of the respective rooms are 
facing the same points of compass as the intakes, so that the 
wind pressure can be depended upon at least to the extent of the 
allowance made for exposure for the room with the smallest head 
available. Assuming the latter to be 35 per cent., the heat 
required in still weather or the corresponding air volume is only 
74 per cent, of the maximum amount, and the pressure to create 
the reduced flow figures only .74^ = . 55 of the total necessary 
to overcome the resistances of the filter, coil, ducts, stacks, and 
flues at full load. The balance of 45 per cent, would be made 
up, when needed, by wind -pressure. 

It is not safe, however, to figure on the aid of wind pressure to 
the full extent in every case, since the draught power is also 
affected by the flue temperature, which, in turn, is influenced by 
the speed of the air passing the stacks. Again, the heat supply 
to the surfaces may be reduced and thereby the buoyancy. It 
should be remembered further, that in a system with several 
flues having radically different available pressures, the distribu- 
tion will be materially disturbed in the absence of wind, but some- 
times this disadvantage must be accepted when the resistances 
are too great to be overcome by gravity alone, with reasonable 
flue sizes. 

The effective pressures due to heat available for the three flues 
in the present example, as taken from the chart, are .125,. 162, 
and .270 lb. respectively, the lowest head being naturally that for 
the first floor. In this case the .125 lb. represent about 64 per 
cent, of the total pressure that may be depended upon, which is 
.195 lb., including .07 lb. for wind pressure. This is counting 
on 25 per cent, for exposure, or a volume reduced to 80 per cent, 
in still weather. In order to assure fair distribution to the three 
rooms, the branch ducts leading to them are equalized as nearly 
as possible with the stated outside pressure and carrying the full 
volumes. The zone where the wind action is neutralized falls in 
this case between the filter and the tempering coil, allowing con- 
siderable leeway before an extra pressure would put the flues with 
greater resistance under a disadvantage. Of the varying total 
pressure for each flue an equal portion is used up to a certain 
point. The larger this portion, used in the common duct, the 
greater will be the relative difference of head left available for the 



HEATING AND VENTILATING BY GRAVITY 161 

individual flues, and the greater their discrepancies in size. With- 
out wind pressure the distribution is unbalanced the other way, 
the flues with the lightest draught being handicapped. It is 
possible, of course, to overcome these variations in delivery by 
temporary throttling, to suit weather conditions, or other forms 
of regulation, but a well balanced system will always require less 
attention in this respect and be more satisfactory. Pressures 
available, resistances, space, and other conditions should decide 
in each case how far the wind pressure ought to be depended upon. 

If the various items of friction and obstruction in the example 
are checked up, it will be seen, that the entrance loss includes 
that of a screen on the end of a straight duct, plus the head- 
way spent in entering the filter chamber. The entrance to the 
coil casing is a negligible item owing to the low velocity. The 
contraction to the size of the main duct, however, is taken into 
account. The inlets and outlets of stack casings have one side 
flush with the duct, and three sides at right angles, hence they 
will present only about two-thirds of the resistance of a flanged 
duct end. The stack sections are estimated to be equivalent 
to an 8-row coil with 50 per cent, free area, except that for 
the third floor where extra wide spacing is not needed. The 
latter is assumed equal to a 10-row coil with 50 per cent, clear 
space which is about equivalent to 8-rows with 40 per cent, net 
area. 

The losses of head have been figured without allowance for 
temperature, since, in this case, the deduction would about 
offset the additions. 



11 



